Control of toroidal continuously variable transmission

ABSTRACT

The trunnion ( 23 ) of a vehicle toroidal continuously variable transmission is displaced by a step motor ( 52 ) via a control valve ( 56 ) and oil pressure servo cylinder ( 50 ) in order to vary a speed ratio of the transmission. A controller ( 80 ) calculates a target value (z*) of a control variable (z)based on an accelerator pedal depression amount (APS) and output disk rotation speed (ω c0 ) (S 5 ). Further, a time-variant coefficient (f) showing the relation between the trunnion displacement (y) and variation rate (φ) of the gyration angle (φ) of the power roller, is calculated (S 10 ). The error between the speed change response of the transmission and a target linear characteristic can be decreased by determining a command value (u) to the step motor ( 52 ) under a control gain determined based on a time differential (f) of the coefficient (f) (S 20 ).

FIELD OF THE INVENTION

[0001] This invention relates to control of a toroidal continuouslyvariable transmission.

BACKGROUND OF THE INVENTION

[0002] Tokkai 2000-18373 published by the Japanese Patent Office in 2000discloses a feedback control device of a toroidal continuously variabletransmission (hereafter, referred to as TCVT).

[0003] This control device controls a real speed ratio to a target speedratio using a mechanical feedback device which feeds back thedisplacement of a power roller to an oil pressure system that causes thepower roller to displace, and a feedback controller which performsproportional/integral/differential (PID) control of the oil pressuresystem based on the difference between the real speed ratio and thetarget speed ratio.

[0004] The speed ratio of the TCVT varies according to the gyrationangle of the power roller, but this relation is not linear. Thus, thiscontrol device expresses a relation between the displacement of thepower roller and the speed ratio as a second differential derivative,and calculates a transfer function from the target speed ratio to thereal speed ratio by the second differential derivative. By suitablysetting various constants in the transfer function, stability ofresponse of speed ratio control is obtained and overshoot is prevented.

SUMMARY OF THE INVENTION

[0005] In this control device, in calculating the transfer function fromthe second differential derivative, a differential of a time-variantfactor representing the relation between the displacement and thegyration angular velocity of the power roller, and a differential of afirst order partial differential derivative that represents the relationbetween the gyration angle and controlled variables, are both consideredto be zero.

[0006] However, it is not correct to consider these time differentialsto be zero from the viewpoint of speed change response in the speedchange transient stage. For example, if it is considered that a timedifferential is zero when the target speed ratio varies from a smallspeed ratio to a large speed ratio, in the early stages of the speedratio variation of the TCVT, the speed change response will exceed thelinear characteristic defined by the transfer function, and in thelatter half of the speed change variation, the speed change response isless than the linear characteristic defined by the transfer function.When the target speed ratio varies from a large speed ratio to a smallspeed ratio, the reverse phenomenon occurs. This error is more evident,the larger the speed change rate.

[0007] It is therefore an object of this invention to reduce the errorbetween the speed change response of the toroidal continuously variabletransmission, and the target linear characteristic.

[0008] In order to achieve the above object, this invention provides acontrol device of a toroidal continuously variable transmission for avehicle. The vehicle comprises an accelerator pedal. The toroidalcontinuously variable transmission comprises an input disk, an outputdisk, a power roller which transmits torque between the input disk andthe output disk, and a trunnion which supports the power roller free torotate. The trunnion comprises a trunnion shaft and the power rollervaries a gyration angle (φ) according to a displacement (y) of thetrunnion in the direction of the trunnion shaft to vary a speed ratio ofthe input disk and output disk. The transmission further comprises anoil pressure actuator which drives the trunnion in the direction of thetrunnion shaft.

[0009] The control device comprises a control valve which supplies oilpressure to the oil pressure actuator, a mechanical feedback mechanismconnecting the trunnion and the control valve to feed back thedisplacement of the trunnion to the control valve, a valve actuatorwhich controls the control valve according to a command value (u), asensor which detects a rotation speed (ω_(c0)) of the output disk, asensor which detects a depression amount (APS) of the accelerator pedal,a sensor which detects the gyration angle (φ) of the power roller, asensor which detects the displacement (y) of the trunnion in thedirection of the trunnion shaft, and a programmable controller.

[0010] The controller is programmed to calculate a target controlvariable (z*) which is a target value of a control variable (z) being anobject of control, based on the accelerator pedal depression amount(APS) and the output disk rotation speed (ω_(c0)), calculate atime-variant coefficient (f) representing the relation between thedisplacement (y) of the trunnion in the direction of the trunnion shaftand a variation rate (φ) of the gyration angle (φ) of the power roller,calculate a first time differential (f) which is a time differential ofthe time-variant coefficient (f), and determine the command value (u) byapplying a control gain based on the first time differential (f).

[0011] This invention also provides a control method of a toroidalcontinuously variable transmission for a vehicle. The vehicle comprisesan accelerator pedal. The toroidal continuously variable transmissioncomprises an input disk, an output disk, a power roller which transmitstorque between the input disk and the output disk, and a trunnion whichsupports the power roller free to rotate. The trunnion comprises atrunnion shaft and the power roller varies a gyration angle (φ)according to a displacement (y) of the trunnion in the direction of thetrunnion shaft to vary a speed ratio of the input disk and output disk.The transmission further comprises an oil pressure actuator which drivesthe trunnion in the direction of the trunnion shaft, a control valvewhich supplies oil pressure to the oil pressure actuator, a mechanicalfeedback mechanism connecting the trunnion and the control valve to feedback the displacement of the trunnion to the control valve, and a valveactuator which controls the control valve according to a command value(u).

[0012] The control method comprises detecting a rotation speed (ω_(c0))of the output disk, detecting a depression amount (APS) of theaccelerator pedal, detecting the gyration angle (φ) of the power roller,detecting the displacement (y) of the trunnion in the direction of thetrunnion shaft, calculating a target control variable (z*) which is atarget value of a control variable (z) being an object of control, basedon the accelerator pedal depression amount (APS) and the output diskrotation speed (φ_(c0)), calculating a time-variant coefficient (f)representing the relation between the displacement (y) of the trunnionin the direction of the trunnion shaft and a variation rate (φ) of thegyration angle (φ) of the power roller, calculating a first timedifferential (f) which is a time differential of the time-variantcoefficient (f) and determining the command value (u) by applying acontrol gain based on the first time differential (f).

[0013] The details as well as other features and advantages of thisinvention are set forth in the remainder of the specification and areshown in the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014]FIG. 1 is a schematic diagram of a toroidal continuously variabletransmission (TCVT) to which this invention is applied.

[0015]FIG. 2 is a schematic diagram of a drive mechanism of a powerroller of the TCVT.

[0016]FIG. 3 is a schematic diagram of a speed ratio control deviceaccording to this invention.

[0017]FIG. 4 is a block diagram describing the function of aprogrammable controller according to this invention.

[0018]FIG. 5 is a diagram showing the characteristics of a map stored bythe controller, specifying the relation between a gyration angle and aspeed ratio.

[0019]FIG. 6 is a diagram showing the characteristics of a map stored bythe controller, specifying the relation between a vehicle speed VSP, afinal input rotation speed tω₁ and an accelerator pedal depressionamount APS.

[0020]FIGS. 7A and 7B are flowcharts describing a speed ratio controlroutine performed by the controller.

[0021] FIGS. 8A-8C are diagrams showing the characteristics of a map ofthe parameters a₁, a₂, g stored by the controller.

[0022]FIG. 9 is a schematic diagram of an infinitely variabletransmission according to which a second embodiment of this invention isapplied.

[0023]FIG. 10 is a block diagram describing the function of thecontroller according to a third embodiment of this invention.

[0024]FIGS. 1A and 1B are similar to FIGS. 7A and 7B, but showing thethird embodiment of this invention.

[0025]FIG. 12 is a block diagram describing the function of thecontroller according to a fourth embodiment of this invention.

[0026] FIGS. 13A-13C are diagrams which graphically represent the speedratio control of the controller according to the fourth embodiment ofthis invention.

[0027]FIG. 14 is a flowchart describing the speed ratio control routineperformed by the controller according to the fourth embodiment of thisinvention.

[0028]FIG. 15 is a block diagram describing the function of thecontroller according to a fifth embodiment of this invention.

[0029]FIG. 16 is a diagram which graphically represents the speed ratiocontrol of the controller according to a sixth embodiment of thisinvention.

[0030]FIG. 17 is a block diagram describing the function of thecontroller according to the sixth embodiment of this invention.

[0031]FIGS. 18A and 18B are flowcharts describing the speed ratiocontrol routine performed by the controller according to the sixthembodiment of this invention.

[0032]FIG. 19 is a block diagram describing the function of thecontroller according to a seventh embodiment of this invention.

[0033]FIGS. 20A and 20B are flowcharts describing the speed changecontrol routine performed by the controller according to the seventhembodiment of this invention.

[0034]FIG. 21 is a timing chart describing a response delay in the speedratio control according to a prior art.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0035] Referring to FIG. 1 of the drawings, a toroidal continuouslyvariable transmission (TCVT) 10 which applies this invention isconnected to the engine of a vehicle via a torque converter 12. Thetorque converter 12 is provided with an impeller 12A, a turbine runner12B, a stator 12C, a lock up clutch 12D, and an output rotation shaft14.

[0036] The TCVT 10 comprises a hollow torque transmission shaft 16disposed coaxially with the output rotation shaft 14.

[0037] The torque transmission shaft 16 is supported in a housing 22such that it can displace to some extent in the axial direction. TheTCVT 10 is provided with a first toroidal unit 18 and a second toroidalunit 20 which are formed on the torque transmission shaft 16.

[0038] The first toroidal unit 18 is provided with an input disk 18A, anoutput disk 18B, and a pair of power rollers 18C, 18D gripped betweenthese disks.

[0039] The second toroidal unit 20 is provided with an input disk 20A,an output disk 20B, and a pair of power rollers 20C, 20D gripped betweenthese disks.

[0040] The power rollers 18C, 18D transfer a rotation of the input disk18A to the output disk 18B at an arbitrary speed ratio according to thegyration angle. The power rollers 20C, 20D transfer a rotation of theinput disk 20A to the output disk 20B at an arbitrary speed ratioaccording to the gyration angle.

[0041] The input disk 18A is connected to the torque transmission shaft16 via a ball spline 24, and the input disk 18B is connected to thetorque transmission shaft 16 via a ball spline 26, such that somedisplacement is permitted in the axial direction, respectively.

[0042] The output disks 18B, 20B are formed in one piece, and aresupported free to rotate relative to the torque transmission shaft 16.An output gear 28 is fixed to the output disks 18B, 20B. The rotation ofthe output gear 28 is transmitted to drive wheels of the vehicle via acounter gear 30A, a counter shaft 30 and other gears.

[0043] A forward/reverse change-over mechanism 40 and a loading cammechanism 34 are disposed between the output rotation shaft 14 andtorque transmission shaft 16. The forward/reverse change-over mechanism40 is provided with a double planet planetary gear set 42, a forwardclutch 44 and a reverse brake 46.

[0044] The planetary gear set 42 comprises two groups of planet gears42D, 42E, between a sun gear 42C and a ring gear 42B. The ring gear 42Bis connected with the output rotation shaft 14. The planet gears 42D aresupported by a carrier 42A, and the planet gears 42E are supported by acarrier 42F.

[0045] The forward clutch 44 engages or releases the carrier 42A andoutput rotation shaft 14. The reverse brake 46 engages the ring gear 42Bwith the housing 22 and releases the ring gear 42B therefrom. Thecarrier 42E is connected with a drive disk 34B of the loading cammechanism 34. The drive disk 34B is fixed to the torque transmissionshaft 16.

[0046] A forward/reverse change-over mechanism 40 engages the forwardclutch 44, and transmits the rotation of the engine to drive disk 34B asit is by releasing the reverse brake 46. Conversely, when the forwardclutch 44 is released while engaging the reverse brake 46, the rotationof the engine is reversed and transmitted to the drive disk 34B.

[0047] The loading cam mechanism 34 comprises a cam roller 34A which isinterposed between the drive disk 34A and input disk 18A. The cam roller34A exerts an axial force on the input disk 18A according to therotation of drive disk 34B, and makes the input disk 18A rotate togetherwith the drive disk 34A. The cam roller 34A exerts an axial force on theinput disk 18A, and also exerts a force in the reverse direction on thetorque transmission shaft 16 due to the reaction. This force istransmitted to the input disk 20A via a plate spring 38. As a result,the input disk 18A is pushed towards the output disk 18B, and the inputdisk 20A is pushed towards the output disk 20B.

[0048] Next, referring to FIG. 2, the power rollers 20C, 20D aresymmetrically disposed on both sides of the torque transmission shaft16. The power rollers 18C, 18D are similarly disposed.

[0049] The power rollers 20C, 20D are supported by trunnions 23,respectively. A servo piston 51 of an oil pressure servo cylinder 50 isconnected with the trunnion 23 via a trunnion shaft 23D. The servopiston 51 causes the trunnion 20C to displace in the direction of thetrunnion shaft 23D according to the differential pressure of the oilpressures applied to the oil chambers 50A, SOB.

[0050] The oil chamber 50A is connected to a port 56H of a shift controlvalve 56, and an oil chamber 50B is connected to a port 56L of the shiftcontrol valve 56. The shift control valve 56 is provided with a spool56S connected with a step motor 52 via a link 53. The shift controlvalve 56 supplies line pressure to one of the ports 56H, 56L andreleases the pressure on the other to the drain according to thedisplacement of the spool 56S, thereby generating the differentialpressure of the oil chambers 50A, 50B.

[0051] Of the power rollers 18C, 18D of the first toroidal unit 18 andthe power rollers 20C, 20D of the second toroidal unit 20, only thetrunnion 23 which supports the power roller 20C is connected to amechanical feedback device which feeds back the axial displacement androtational displacement of the trunnion 23 to the spool 56S. Themechanical feedback device is provided with a precess cam 55 fixed tothe trunnion shaft 23D, and a link 54 which transmits the displacementof the precess cam 55 to the link 53.

[0052] The speed ratio of the TCVT 10 varies according to the gyrationangle of the power rollers 18C, 18D, 20C, 20D. In order to change thegyration angle of the power rollers 18C, 18D, 20C, 20D, the trunnion 23is driven in the direction of the trunnion shaft 23D by operation of theshift control valve 56. Consequently, the moment around the trunnionshaft 23D which the input disk 18A (20A) and output disk 18B (20B) exerton the power rollers 18C, 18D (20C, 20D) varies, and the gyration angleof the power rollers 18C, 18D (20C, 120D) varies.

[0053] Since the power rollers 18C, 18D, 20C, 20D are supported by thetrunnions 23, the trunnions 23 and the trunnion shafts 23D rotate as thegyration angle of the power rollers 18C, 18D, 20C, 20D varies.

[0054] In the steady state, the power rollers 18C (20C) and 18D (20D)are located in the neutral position with respect to the displacementdirection of the trunnion shaft 23. Here, the neutral position is thestate wherein the centers of the rotation axis of the power rollers 18C,18D, 20C, 20D are not offset above or below the center line of thetorque transmission shaft 16. In this state, the spool 56S is maintainedin the neutral position wherein the ports 56H, 56L are not connected tothe line pressure PI or the drain.

[0055] If the spool 56S displaces in the axial direction due to thedrive of the step motor 52, a high pressure will be supplied to eitherof the oil chambers 50A, 50B from the shift control valve 56, and thetrunnion 23 will displace in the direction of the trunnion shaft 23D.Consequently, the gyration angle of the power roller 18C, 18D, 20C, 20Dvaries. The precess cam 55 feeds back this displacement to the spool56S, and displaces the spool 56S in the reverse direction to the drivedirection due to the step motor 52. Consequently, when the gyrationangle of the power rollers 18C, 18D, 20C, 120D corresponding to therotational displacement of the step motor 52 is achieved, the spool 56Sreturns to the neutral position. This mechanical feedback mechanism dueto the precess cam 52 has a damping effect on the variation of the speedratio of the TCVT 10 in the transient state, and suppresses fluctuationof the speed ratio.

[0056] Next, the construction of a speed ratio control device accordingto this invention provided for controlling the speed ratio of the TCVT10 will be described, referring to FIG. 3.

[0057] Speed ratio control of the TCVT 10 is performed by a control of astep signal to a step motor 52, and the speed ratio control device isprovided with a programmable controller 80 for this purpose. Thecontroller 80 comprises a microcomputer provided with a centralprocessing unit (CPU), read only memory (ROM), random access memory(RAM) and I/O interface (I/O interface). The controller may alsocomprise plural microcomputers.

[0058] In order to perform the above control, signals are input to thecontroller 80 from an input rotation speed sensor 84 which detects arotation speed ω_(c1) of the input disks 18A, 20A, an output rotationspeed sensor 83 which detects a rotation speed ω_(c0) of the outputdisks 18B, 20B, a rotation speed sensor 82 which detects a rotationspeed ω_(pr) of the power rollers 18C, 18D, 20C, 20D, a gyration anglesensor 85 which detects a gyration angle φ of the power rollers 18C,18D, 20C, 20D, a position sensor 86 which detects an offset distance yfrom the neutral position of the trunnion 23, an accelerator pedaldepression amount sensor 81 which detects a depression amount APS of anaccelerator pedal with which the vehicle is provided, and a linepressure sensor 87 which detects the line pressure P1, respectively.

[0059] Next, the details of the speed ratio control performed by thecontroller 80 will be described, referring to FIG. 4. The blocks in thisdrawing show the functions of the controller 80 as imaginary units, anddo not imply they physically exist.

[0060] In the TCVT 10, the dynamic characteristics of the variation ofthe gyration angle φ of the power rollers 18C, 18D, 20C, 20D relative tothe displacement u of the step motor 52 are expressed by the followingequations (1), (2) as in the above prior art. As the step motor 52 isdisplaced corresponding to a command value output from the controller80, in the following description, the command value output from thecontroller 80 to the step motor 52, and the resulting displacement ofthe step motor 52, are expressed by an identical symbol u.

{dot over (φ)}=f·y  (1)

{dot over (y)}=g·(u−a ₁ ·φ−a ₂ ·y)  (2)

[0061] where, f=coefficient,

[0062] g=valve gain for converting the position x of the spool 56S intoa speed of axial displacement of the power rollers 18C, 18D, 20C, 20D,and

[0063] a₁, a₂=constants depending on the specifications of the precesscam 52, and links 53, 54.

[0064] The parameters a₁, a₂, g are also dependent on the line pressureP1, so they may be computed using a map obtained beforehand by a systemidentification test etc., and are previously stored in the memory of thecontroller 80 as constants.

[0065] A speed ratio G has the nonlinear characteristic shown in thefollowing equation (3) relative to the gyration angle φ. $\begin{matrix}{G = {{h(\varphi)} = \frac{c_{g0} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}}{C_{g0} - {\cos \quad \varphi}}}} & (3)\end{matrix}$

[0066] where, C_(g0), C_(g1)=constants depending on the construction ofthe TCVT 10.

[0067] A coefficient f is expressed by the following equation (4)depending on the gyration angle φ of the power rollers 18C, 18D, 20C,20D, and the rotation speed ω_(c0) of the output disks 18B, 20B.$\begin{matrix}{{f\left( {\varphi,\omega_{co}} \right)} = {\frac{{\cos \left( {c_{g1} - \varphi} \right)} \cdot \left\{ {c_{g0} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}} \right\}}{cf} \cdot \omega_{co}}} & (4)\end{matrix}$

[0068] where, cf=constant depending on the construction of the TCVT 10.

[0069] Referring to FIG. 4, in order to determine the command value uoutput to the step motor 52, the controller 80 comprises a coefficientcomputing unit 101, a control variable differential computing unit 102,a control error computing unit 103, a partial differential derivativecomputing unit 104, a coefficient differential computing unit 105, anequivalent input computing unit 106, a target control variabledifferential computing unit 108, a control error compensation amountcomputing unit 110, a displacement computing unit 111 and a target valuegenerating unit 109. The partial differential derivative computing unit104 and coefficient differential computing unit 105 form a gaincorrection unit 107.

[0070] The control variable differential computing unit 102, controlerror computing unit 103, equivalent input computing unit 106, targetcontrol variable differential computing unit 108, control errorcompensation amount computing unit 110 and displacement computing unit111 form a command value computing unit 100.

[0071] The coefficient computing unit 101 computes the coefficient fusing the equation (4) from the gyration angle φ and rotation speedω_(c0) of the output disks 18B, 20B. The coefficient f is determined bythe geometry of the toroidal units, and is a time-variant constantexpressing the relation between the axial displacement and the gyrationangular velocity of the power roller.

[0072] The gyration angle φ is detected by a gyration angle sensor 85.The gyration angle φ can also be estimated by an observer, or calculatedby looking up a map shown in FIG. 5 prestored in the controller 80 fromthe speed ratio G calculated by the following equation (5).$\begin{matrix}{G = \frac{\omega_{ci}}{\omega_{co}}} & (5)\end{matrix}$

[0073] The partial differential derivative computing unit 104 calculatesa partial differential derivative $\frac{\partial h}{\partial\varphi}$

[0074] and its time differential$\frac{}{t}{\left( \frac{\partial h}{\partial\varphi} \right).}$

[0075] Here, considering the control variable z to be the speed ratio Gof the TCVT 10, the equation (3) is expressed by the following equation(6). $\begin{matrix}{z = {{h(\varphi)} = \frac{c_{g0} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}}{c_{g0} - {\cos \quad \varphi}}}} & (6)\end{matrix}$

[0076] The partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0077] is expressed by the following equation (7). $\begin{matrix}{\frac{\partial h}{\partial\varphi} = {\frac{\sin \left( {{2 \cdot c_{gi}} - \varphi} \right)}{c_{g0} - {\cos \quad \varphi}} - \frac{\sin \quad {\varphi \cdot \left\{ {c_{g1} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}} \right\}}}{\left( {c_{g0} - {\cos \quad \varphi}} \right)^{2}}}} & (7)\end{matrix}$

[0078] The partial differential derivative computing unit 104 directlycalculates the partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0079] using the equation (7), or calculates the partial differentialderivative $\frac{\partial h}{\partial\varphi}$

[0080] from the gyration angle φ by looking up a map based on theequation (7) that is previously stored in the memory of the controller80.

[0081] The time differential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0082] is given by the following equation (8). $\begin{matrix}{{\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)} = {\frac{\partial^{2}h}{\partial\varphi^{2}} \cdot \overset{.}{\varphi}}} & (8)\end{matrix}$

[0083] Equation (9) is obtained from the equations (1) and (8).$\begin{matrix}{{\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)} = {\frac{\partial h^{2}}{\partial\varphi^{2}} \cdot f \cdot y}} & (9)\end{matrix}$

[0084] $\frac{\partial h}{\partial\varphi}$

[0085] in the equation (9) can be calculated by the following equation(10) by differentiating $\frac{\partial^{2}h}{\partial\varphi^{2}}$

[0086] of the equation (7) with respect to the gyration angle φ.$\begin{matrix}\begin{matrix}{\frac{\partial^{2}h}{\partial\varphi^{2}} = \quad {\frac{\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}{c_{g0} - {\cos \quad \varphi}} - \frac{\sin \quad {\varphi \cdot {\sin \left( {{2 \cdot c_{g1}} - \varphi} \right)}}}{\left( {c_{g0} - {\cos \quad \varphi}} \right)^{2}} -}} \\{\quad {\frac{\cos \quad {\varphi \cdot \left\{ {c_{g0} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}} \right\}}}{\left( {c_{g0} - {\cos \quad \varphi}} \right)^{2}} +}} \\{\quad {\frac{\sin \quad {\varphi \cdot {\sin \left( {2{{\cdot c_{g1}} - \varphi}} \right)} \cdot \left\{ {c_{{g0}\quad} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}} \right\}}}{\left( {c_{g0} - {\cos \quad c_{g0}} - {\cos \quad \varphi^{2}}} \right)} +}} \\{\quad \frac{2{{\cdot \sin^{2}}{\varphi \cdot \left\{ {C_{g0} - {\cos \left( {{2 \cdot c_{g0}} - \varphi} \right)}} \right\}}}}{\left( {c_{g0} - {\cos \quad \varphi}} \right)^{3}}}\end{matrix} & (10)\end{matrix}$

[0087] The partial differential derivative computing unit 104 directlycalculates the time differential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0088] from the gyration angle φ by the equations (9) and (10).Alternatively, a map generated based on the equations (9) and (10) ispreviously stored in the memory of the controller 80 and the partialdifferential coefficient computing unit 104 may obtain the timedifferential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0089] by looking up the map according to the gyration angle φ.

[0090] The coefficient differential computing unit 105 calculates thecoefficient f and the time differential of the coefficient {dot over(f)}, from the gyration angle φ of the power roller, offset distance yof the trunnion 23 form the neutral position, and rotation speed ω_(c0)of the output disks 18B, 20B. The time differential {dot over (f)} ofthe coefficient f is given by the following equation (11).$\begin{matrix}{\overset{.}{f} = {{\frac{\partial f}{\partial\varphi} \cdot \overset{.}{\varphi}} + {\frac{\partial f}{\partial\omega_{co}} \cdot {\overset{.}{\omega}}_{co}}}} & (11)\end{matrix}$

[0091] If the relation of the equation (1) is applied to the equation(11), the following equation (12) will be obtained. $\begin{matrix}{\overset{.}{f} = {{\frac{\partial f}{\partial\varphi} \cdot f \cdot y} + {\frac{\partial f}{\partial\omega_{co}} \cdot {\overset{.}{\omega}}_{co}}}} & (12)\end{matrix}$

[0092] $\frac{\partial f}{\partial\varphi}$

[0093] in the equation (12) is given by the following equation (13)deduced from the equation (4). $\begin{matrix}{\frac{\partial f}{\partial\varphi} = {\frac{{{{\sin \left( {c_{g1} - \varphi} \right)} \cdot \left\{ {c_{g1} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}} \right\}} - \quad {\sin \left( {{2 \cdot c_{g1}} - \varphi} \right)}}{\cdot {\cos \left( {c_{g1} - \varphi} \right)}}}{c_{f}} \cdot \omega_{co}}} & (13)\end{matrix}$

[0094] where, cf. c_(g1)=constants depending on the construction of theTCVT 10.

[0095] The coefficient differential computing unit 105 calculates$\frac{\partial f}{\partial\varphi}$

[0096] using the equation (13) from the gyration angle φ and rotationspeed ω_(c0) of the output disks 18B, 20B or by looking up a mappreviously prepared based on the equation (13).

[0097] On the other hand, $\frac{\partial f}{\partial\omega_{co}}$

[0098] in the equation (12) is expressed by the following equation (14)deduced from equation (4), $\begin{matrix}{\frac{\partial f}{\partial\omega_{co}} = \frac{{\cos \left( {c_{g1} - \varphi} \right)}{\cdot \left\{ {c_{g0} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}} \right\}}}{c_{f}}} & (14)\end{matrix}$

[0099] where, C_(g0)=constant depending on the configuration of the TCVT10.

[0100] The coefficient differential computing unit 105 directlycalculate $\frac{\partial f}{\partial\omega_{co}}$

[0101] based on equation (14), or calculates$\frac{\partial f}{\partial\omega_{co}}$

[0102] from the gyration angle φ by looking up a map that is previouslyprepared based on equation (14).

[0103] The time differential {dot over (ω)}_(c0) of the rotation speedω_(c0) of the output disks 18B, 20B in the equation (12) is calculatedfrom the variation of the rotation speed ω_(c0) for every computationperiod, or is calculated using a pseudo-differentiator. The output disks18B, 20B are influenced by the inertial force of the vehicle, so thetime variation is small. Therefore, the differential {dot over (ω)}_(c0)of the rotation speed ω_(c0) of the output disks 18B, 20B is also smallcompared for example with the variation of the gyration angle φ.According to experiments or simulations by the inventors, there is noproblem in practice even if the time differential {dot over (ω)}_(c0) isregarded as zero.

[0104] The control variable differential computing unit 102 calculates adifferential {dot over (z)} of the control variable z from the offsetdistance y of the trunnion 23 from the neutral position, the coefficientf and the partial differential derivative ∂h/∂φ. The control variable zis a function of the gyration angle φ, so the differential {dot over(z)} of the control variable z is given by the following equation (15).$\begin{matrix}{\overset{.}{z} = {\frac{\partial h}{\partial\varphi} \cdot \overset{.}{\varphi}}} & (15)\end{matrix}$

[0105] The following equation (16) is obtained from the equations (15)and (1). $\begin{matrix}{\overset{.}{z} = {\frac{\partial h}{\partial\varphi} \cdot f \cdot y}} & (16)\end{matrix}$

[0106] The control variable differential computing unit 102 calculatesthe differential {dot over (z)} of the control variable z from equation(16).

[0107] The target value generating unit 109 calculates a target controlvariable z* from the accelerator pedal depression amount APS detected bythe accelerator pedal depression amount sensor 81, and the rotationspeed ω_(c0) of the output disks 18B, 20B detected by the rotation speedsensor 83, by the following process.

[0108] First, the vehicle speed VSP is calculated by multiplying therotation speed ω_(c0) by a constant kv, by equation (17). The constantkv is a constant depending on the gear ratio of a final gear interposedbetween the TCVT 10 and the drive wheels of the vehicle, and the tirediameter.

VSP=kv·ω _(c0)  (17)

[0109] Next, the final input rotation speed to), is calculated from theaccelerator pedal depression amount APS and vehicle speed VSP using amap having the characteristics shown in FIG. 6.

[0110] Next, a final control variable tz is calculated by the followingequation (18) from the final input rotation speed tω₁ and rotation speedω_(c0) of the output disks 18B, 20B. $\begin{matrix}{{tz} = \frac{t\quad \omega_{i}}{\omega_{co}}} & (18)\end{matrix}$

[0111] Finally, the final control variable tz is processed by a lowpassfilter to calculate the target control variable z*. The lowpass filteris represented by the following equation (19).

{dot over (z)}=−c _(t) ·z*+c _(t) ·tz  (19)

[0112] where, c_(t)=cutoff frequency of lowpass filter.

[0113] The target control variable differential computing unit 108computes the differential z* of the target control variable z*.

[0114] The control error computing unit 103 calculates a control error σfrom the control variable z, control variable differential {dot over(z)} and target control variable z*.

[0115] These relations are expressed by the following equation (20).

σ={dot over (z)}+c ₀·(z−z*)  (20)

[0116] where, c₀=first order delay time constant.

[0117] The control variable z is calculated as the speed ratio G of theTCVT 10 using equation (6) from the gyration angle φ of the powerrollers 18C, 18D, 20C, 20D detected by the gyration angle sensor 85.Alternatively, it is calculated using equation (5) from the rotationspeed ω_(c0) of the output disks 18B, 20B and the rotation speed ω_(c1)of the input disks 18A, 20A detected by the input rotation speed sensor84.

[0118] The relation between the control variable z, control variabledifferential {dot over (z)} and target control variable z* when thecontrol error a is zero is expressed by the following equation (21).

{dot over (a)}=−c ₀ ·z+c ₀ ·z*  (21)

[0119] The equation (21) shows that the control variable z has a firstorder delay relative to the target control variable z* when the controlerror σ is zero.

[0120] The control error compensation amount computing unit 110calculates a control error compensation amount u_(sw) using thefollowing equation (22) from the control error σ. $\begin{matrix}{u_{sw} = {{- k} \cdot \frac{\sigma}{\sigma }}} & (22)\end{matrix}$

[0121] where, k=switching gain.

[0122] If the switching gain k is set large, the control error σ willconverge to zero in a finite time. The target control variabledifferential computing unit 108 calculates the target control variabledifferential {dot over (z)}* from the target control variable z*. Thiscalculation is performed by processing the target control variable z* bya pseudo-differentiator, or by using the equation (19).

[0123] The equivalent input computing unit 106 calculates an equivalentinput u_(eq) equivalent to the command signal to the step motor 52 whenthe control error σ is a fixed value, from the gyration angle φ of thepower rollers 18C, 18D, 20C, 20D, the offset distance y of the trunnion23 from the neutral position, the target control variable differential{dot over (z)}* and the coefficient f.

[0124] Therefore, both sides of the equation (20) are differentiated toobtain the following equation (23).

{dot over (σ)}={umlaut over (z)}+c _(O) ·{dot over (z)}−c ₀ ·{dot over(z)}*  (23)

[0125] When the control error a is fixed, the control error differential{dot over (σ)} is zero. Therefore, equation (23) is replaced by thefollowing equation (24).

{umlaut over (z)}=−c ₀ ·{dot over (z)}+c ₀ ·{dot over (z)}*  (24)

[0126] On the other hand, if both sides of the equation (16) aredifferentiated, the following equation (25) is obtained. $\begin{matrix}{\overset{¨}{z} = {{\frac{}{t}{\left( \frac{\partial h}{\partial\varphi} \right) \cdot f \cdot y}} + {\frac{\partial h}{\partial\varphi} \cdot \overset{.}{f} \cdot y} + {\frac{\partial h}{\partial\varphi} \cdot f \cdot \overset{.}{y}}}} & (25)\end{matrix}$

[0127] If the equation (2), equation (16), equation (24) and equation(25) are solved for the command value u of the step motor 52, thefollowing equation (26) is obtained. $\begin{matrix}{u = {{\left\{ {a_{2} - \frac{\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)}{\frac{\partial h}{\partial\varphi} \cdot g} - \frac{\overset{.}{f}}{f \cdot g}} \right\} \cdot y} - {\frac{c_{0}}{\frac{\partial h}{\partial\varphi} \cdot f \cdot g} \cdot \left( {\overset{.}{z} - {\overset{.}{z}}^{*}} \right)} + {a_{1} \cdot \varphi}}} & (26)\end{matrix}$

[0128] The equivalent input computing unit 106 calculates the commandvalue u of the step motor 52 using the differential {dot over (f)} ofthe coefficient f and the time differential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0129] of the partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0130] which were considered to be zero in the above mentioned prior artexample by equation (26), and this is input into the displacementcomputing unit 111 as the equivalent input u_(eq). For the purpose ofthe calculation of equation (26), the partial differential derivativecomputing unit 104 of the gain correction unit 107 calculates the timedifferential${\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)},$

[0131] and the coefficient differential computing unit 105 of the gaincorrection unit 107 calculates the differential {dot over (f)}.

[0132] As long as there is no external disturbance and there is noparameter error, the equivalent input u_(eq) calculated in the equation(26) makes the control error differential {dot over (σ)} zero. In otherwords, if we make the control error σ in the initial state zero, thecontrol error remains zero due to the equivalent input u_(eq).Therefore, the relation between the control variable z and targetcontrol variable z* is given by the equation (24).

[0133] The displacement computing unit 111 outputs the sum of thecontrol error compensation amount u_(sw) calculated by the control·errorcompensation amount computing unit 110 and the equivalent input u_(eq)calculated by the equivalent input computing unit 106, to the step motor52 of the TCVT 10 as a step motor displacement command value u.

[0134] When there is an external disturbance or a parameter error, thecontrol error σ does not become zero with the equivalent input u_(eq)alone. The control error σ is maintained at zero by using the controlerror compensation amount u_(sw) of a magnitude sufficient forcompensating the disturbance and parameter error. As long as the controlerror a is maintained at zero, the control variable z and target controlvariable z* maintain the relation of the equation (21). That is, thedynamic characteristics of the control variable z relative to the targetcontrol variable z* are linear characteristics shown by the equation(21).

[0135] The controller 80 performs the above control by executing thespeed ratio control routine shown in FIGS. 7A and 7B. This routine isperformed at an interval of twenty milliseconds.

[0136] Referring to FIG. 7A, first in a step S1, the controller 80 readsthe gyration angle φ of the power rollers 18C, 18D, 20C, 20D, the offsetdistance y of the trunnion 23 from the neutral position, the acceleratorpedal depression amount APS, the rotation speed ω_(c0) of the outputdisks 18B, 20B, the rotation speed ω_(c1) of the input disks 18A, 20Aand line pressure P1 from the signals input from the sensors.

[0137] Here, the relations shown by the following equations (27), (28)exist between the rotation speed ω_(c0) of the output disks 18B, 20B,the rotation speed ω_(pr) of the power rollers 18C, 18D, 20C, 20D, andthe rotation speed ω_(c1) of the input disks 18A, 20A. $\begin{matrix}{\omega_{ci} = {\frac{c_{g0} - {\cos \left( {c_{g1} - \varphi} \right)}}{c_{g0} - {\cos \quad \varphi}} \cdot \omega_{co}}} & (27) \\{\omega_{pr} = {\frac{c_{g0} - {\cos \left( {c_{g1} - \varphi} \right)}}{c_{g2}} \cdot \omega_{co}}} & (28)\end{matrix}$

[0138] where c_(g0), c_(g1), c_(g2)=constants depending on theconstruction of the TCVT 10.

[0139] Therefore, if two of the four parameters, the rotation speedω_(c0) of the output disks 18B, 20B, the rotation speed ω_(pr) of thepower rollers 18C, 18D, 20C, 20D, the rotation speed ω_(c1) of the inputdisks 18A, 18B and the gyration angle φ of the power rollers 18C, 18D,20C, 20D are known, the two remaining parameters may be calculated bythe equations (27), (28).

[0140] Now, in a following step S2, the controller 80 calculates thevehicle speed VSP by the equation (17).

[0141] In a following step S3, the final input rotation speed tω₁ isdetermined by looking up the map of FIG. 6 from the accelerator pedaldepression amount APS and vehicle speed VSP.

[0142] In a following step S4, the final control variable tz iscalculated by the equation (18), from the final input rotation speed tω₁and the rotation speed ω_(c0) of the output disks 18B, 20B.

[0143] In a following step S5, the target control variable {dot over(z)}* is obtained by processing the final control variable tz by thelowpass filter of the equation (19).

[0144] In a following step S6, the differential {dot over (z)}* of thetarget control variable z* is calculated. The difference between theimmediately preceding value z*⁻¹ of the target control variable z*calculated on the immediately preceding occasion the routine wasexecuted and the target control variable z* calculated on the presentoccasion may be considered as the differential {dot over (z)}*, or thetarget control variable z* may be differentiated using apseudo-differentiator.

[0145] In a following step S7, the control variable z is calculated fromthe rotation speed ω_(c1) of the input disks 18A, 20A, and the rotationspeed ω_(c0) of the output disks 18B, 20B. As mentioned above, thecontrol variable z can be considered to be the speed ratio G of the TCVT10. Therefore, the control variable z can be calculated by the equation(5).

[0146] In a following step S8, the rotation acceleration {dot over(ω)}_(c0) of the output disks 18B, 20B is calculated. This calculationcan be performed by the equation (29) using the difference between thepreceding value of the rotation speed ω_(c0−1) of the output disks 18B,20B read on the immediately preceding occasion the routine was executed,and the rotation speed ω_(c0) of the output disks 18B, 20B read on thepresent occasion the routine is executed. The calculation can beperformed using a pseudo-differentiator or an observer. $\begin{matrix}{{\overset{.}{\omega}}_{co} = \frac{\omega_{c0} - \omega_{{co} - 1}}{T}} & (29)\end{matrix}$

[0147] where, T=execution interval of the routine=twenty milliseconds.

[0148] In a following step S9, the partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0149] is calculated by the equation (7) from the gyration angle φ ofthe power rollers 18C, 18D, 20C, 20D. The time differential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0150] is calculated by the equation (9).$\frac{\partial f}{\partial\varphi}$

[0151] is calculated by the equation (13), and$\frac{\partial f}{\partial\omega_{co}}$

[0152] is calculated by the equation (14). These calculations mayalternatively be performed by looking up maps prestored in thecontroller 80.

[0153] In a following step S10, the coefficient f is calculated by theequation (4) from the rotation speed ω_(c0) of the output disks 18B,20B, and the gyration angle φ of the power rollers 18C, 18D, 20C, 20D.The time differential {dot over (f)} of the coefficient f is calculatedby the equation (12) using the coefficient f, offset distance y of thetrunnion 23 from the neutral position, rotation acceleration {dot over(ω)}_(c0) of the output disks 18B, 20B calculated in the step S8, andpartial differential derivatives$\frac{\partial f}{\partial\varphi}\quad {and}\quad \frac{\partial f}{\partial\omega_{co}}$

[0154] calculated in the step S9.

[0155] As mentioned above, in this calculation, the rotationacceleration {dot over (ω)}_(c0) of the output disks 18B, 20B may beregarded as zero.

[0156] In a following step S11, the control variable differential {dotover (z)} is calculated using the equation (16) from the partialdifferential derivative $\frac{\partial h}{\partial\varphi}$

[0157] calculated in the step S9, coefficient f, and offset distance yof the trunnion 23 from the neutral position.

[0158] Next, referring to FIG. 7B, in a step S12 following the step S11,the controller 80 calculates control error σ using the equation (20)from the control variable differential z calculated in the step S11, thecontrol variable z calculated in the step S7 and the target controlvariable z* calculated in the step S5.

[0159] The processing of steps S13 to step S17 is related to thecalculation of the control error compensation amount u_(sw) by theequation (22).

[0160] First, in the step S13, the controller 80 determines whether ornot the control error σ is a negative value. When the control error σ isa negative value, the controller 80 performs the processing of the stepS14. When the control error σ is not a negative value, the controller80, in the step S15, determines whether or not the control error σ is apositive value. When the control error σ is a positive value, thecontroller 80 performs the processing of the step S16, and when thecontrol error σ is not a positive value, i.e., in the case of zero, itperforms the processing of the step S17.

[0161] In the step S14, the control error compensation amount u_(sw) isset equal to a constant k. The constant k is a value corresponding tothe maximum displacement amount of the step motor 52. In the step S16,the control error compensation amount u_(sw) is set equal to a constant−k. In the step S17, the control error compensation amount u_(sw) is setto zero.

[0162] After determining the control error compensation amount u_(sw) inthis way, in a step S18, the controller 80 calculates the parameters a₁,a₂, g by looking up maps having the characteristics shown in FIGS. 8A-8Cfrom the line pressure P1. These maps are prestored in the memory of thecontroller 80.

[0163] In the following step S19, the command value u to the step motor52 is calculated using the equation (26), and the equivalent inputu_(eq) is set equal to the computed command value u.

[0164] In a final step S20, the controller 80 outputs the sum of thecontrol error compensation amount u_(sw) and equivalent input u_(eq) asthe command value u to the step motor 52.

[0165] After processing of the step S20, the controller 80 terminatesthe routine.

[0166] Due to this control routine, an effectively fixed speed changeresponse is obtained regarding speed ratio variation towards a certaintarget speed ratio regardless of the present speed ratio or thevariation amount between the present speed ratio and the target speedratio.

[0167] Next, a second embodiment with respect to the control of thespeed ratio of an infinitely variable transmission (IVT) will bedescribed, referring to FIG. 9.

[0168] The IVT comprises an IVT input shaft 1A, a TCVT 10 similar to thefirst embodiment, a fixed speed ratio transmission 3, a planetary gearset 6 and an IVT output shaft 5. The IVT input shaft 1A is joined to theengine, and rotates together with the torque transmission shaft 16 ofthe TCVT 10.

[0169] The fixed speed ratio transmission 3 comprises an input gear 3Awhich meshes with the input gear 3A fixed to the IVT input shaft 1A, andoutput gear 3B which is supported by the IVT output shaft 5 free torotate.

[0170] The TCVT 10 essentially has the same construction as that of theTCVT 10 of the first embodiment, however it differs in that an outputsprocket 28A is provided instead of the output gear 28.

[0171] The rotation of the output sprocket 28A is transmitted to the IVToutput shaft 5 via a chain 4B on a sprocket 4A supported free to rotateon the IVT output shaft 5.

[0172] The planetary gear set 6 is provided with a sun gear 62Aconnected with the sprocket 4A, a carrier 62B connected with the outputgear 3B of the fixed speed ratio transmission 3 via a powerrecirculation clutch 9, and a ring gear 62C fixed to the IVT outputshaft 5. The sun gear 62A is an external contact gear, the ring gear 62Cis an internal contact gear, and the carrier 62B supports plural planetgears 62D interposed between these gears such that they are free torotate and turn around the outer circumference of the sun gear 62A.

[0173] The sun gear 62A is supported free to rotate on the IVT outputshaft 5 in the same way as the sprocket 4A. The sprocket 4A is connectedwith the IVT output shaft 5 via a direct clutch 7.

[0174] The direct clutch 7 is engaged or disengaged by a first servoactuator 92 according to the oil pressure supplied from a first solenoidvalve 91. The power recirculation clutch 9 is engaged or disengaged by asecond servo actuator 93 according to the oil pressure supplied from asecond solenoid valve 94. In a direct mode, wherein the direct clutch 7is engaged and the power recirculation clutch 9 is disengaged, the poweroutput of the TCVT 10 is output to the IVT output shaft 5 as it is viathe direct clutch 7. In the power recirculation mode, wherein the directclutch 7 is disengaged and the power recirculation clutch 9 is engaged,the rotation of a ring gear 62C is output by the IVT output shaft 5according to the relative rotation of the carrier 62B connected with theoutput gear 3B of the fixed speed ratio transmission 3, and the sun gear62A connected with the output sprocket 28A of the TCVT 10.

[0175] The dynamic characteristics of the variation of the gyrationangle φ of the power rollers 18C, 18D, 20C, 20D relative to thedisplacement u of the step motor are expressed by the equation (1) andequation (2) as in the first embodiment.

[0176] The speed ratio i of the IVT in the power recirculation mode isexpressed by the following equation (30). $\begin{matrix}{i = \frac{c_{g2} \cdot \left( {c_{g0} - {\cos \quad \varphi}} \right)}{{c_{g3} \cdot \left( {c_{g0} - {\cos \quad \varphi}} \right)} - {c_{g4} \cdot \left\{ {c_{g0} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}} \right\}}}} & (30)\end{matrix}$

[0177] where, C_(g0), C_(g1), C_(g2), C_(g3), C_(g4)=constants dependingon the construction of the IVT.

[0178] In the direct mode, the output of the TCVT 10 is the output ofthe IVT, so the IVT speed ratio i has the same characteristics as thespeed ratio G of the equation (3).

[0179] Therefore, in the speed ratio control of the IVT, the controldepending on the equation (30) and control depending on the equation (3)are changed over according to the operating mode.

[0180] The control variable z may be the IVT speed ratio i, or theinverse i_(i) of the IVT speed ratio i. The partial differentialderivative of the control variable z with respect to the gyration angleφ changes with these differences, but the partial differentialderivative can easily be calculated by partially differentiating thecontrol variable z with respect to the gyration angle φ. Therefore, thecalculation of the partial differential derivative is not described indetail here.

[0181] The control variable z in the power recirculation mode when thecontrol variable z is the IVT speed ratio i, is expressed by thefollowing equation (31). $\begin{matrix}{z = {{h_{ip}(\varphi)} = \frac{c_{g2} \cdot \left( {c_{g0} - {\cos \quad \varphi}} \right)}{{c_{g3} \cdot \left( {c_{g0} - {\cos \quad \varphi}} \right)} - {c_{g4} \cdot \left\{ {c_{g0} - {\cos \quad \left( {{2 \cdot c_{g1}} - \varphi} \right)}} \right\}}}}} & (31)\end{matrix}$

[0182] The control variable z in the direct mode when the controlvariable z is the IVT speed ratio i, is expressed by the equation (6)deduced from the equation (3).

[0183] The controller 80 first calculates, in the target valuegenerating unit 109 of FIG. 4, an IVT output shaft rotation speedω_(l0). In the power recirculation mode, it is calculated from therotation speed ω_(c0) of the output disk 18B, 20B and a gear ratio ofthe planetary gear set 6. In the direct mode, it is calculated bymultiplying the rotation speed ω_(c0) of the output disk 18B, 20B by apredetermined factor.

[0184] Next, the final input rotation speed tω_(t) is calculated fromthe accelerator pedal depression amount APS and vehicle speed VSP usingthe map of FIG. 6. The final control variable tz is then calculated bythe following equation (32). $\begin{matrix}{{tz} = \frac{t\quad \omega_{i}}{\omega_{io}}} & (32)\end{matrix}$

[0185] On the other hand, the control variable z in the powerrecirculation mode when the control variable z is the inverse i₁ of theIVT speed ratio i, is expressed by the following equation (33).$\begin{matrix}{z = {{h_{iip}(\varphi)} = {c_{g5} - {c_{g6} \cdot \frac{c_{g0} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}}{c_{g0} - {\cos \quad \varphi}}}}}} & (33)\end{matrix}$

[0186] where, C_(g5), C_(g6)=constants depending on the construction ofthe IVT.

[0187] The control variable z in the direct mode when the controlvariable z is the inverse i₁ of the IVT speed ratio i, is expressed bythe following equation (34). $\begin{matrix}{z = {{h_{iid}(\varphi)} = \frac{c_{g0} - {\cos \quad \varphi}}{c_{g0} - {\cos \left( {{2 \cdot c_{g1}} - \varphi} \right)}}}} & (34)\end{matrix}$

[0188] When the control variable z is the inverse i_(l) of the IVT speedratio, the controller 80 calculates, in the target value generating unit109 of FIG. 4, the final input rotation speed tω_(l) and IVT outputrotation speed ω_(l0) as described above. Then, the controller 80calculates the final control variable tz from the final input rotationspeed tω_(l) and the IVT output rotation speed ω_(l0) by the followingequation (35). $\begin{matrix}{{tz} = \frac{\omega_{io}}{t\quad \omega_{i}}} & (35)\end{matrix}$

[0189] The process for obtaining the target control variable z* from thefinal control variable tz is identical to that of the first embodiment.

[0190] Thus, in the IVT, as in the TCVT of the first embodiment, anessentially fixed speed change response is obtained for the speed ratiovariation relative to a certain target speed ratio regardless of thepresent speed ratio or the variation amount between the present speedratio and the target speed ratio.

[0191] Here, the difference between the first and second embodimentsaccording to this invention, and the above mentioned prior art examplewill be described.

[0192] In the prior art example, a second differential with respect totime of the equation (3) was calculated, and the equation (1) andequation (2) were substituted to obtain the following equation (36).$\begin{matrix}{\overset{¨}{G} = {{\frac{}{t}{\left( \frac{\partial h}{\partial\varphi} \right) \cdot f \cdot y}} + {\frac{\partial h}{\partial\varphi} \cdot \overset{.}{f} \cdot y} + {\frac{\partial h}{\partial\varphi} \cdot f \cdot g \cdot \left( {u - {a_{i} \cdot \varphi} - {a_{2} \cdot y}} \right)}}} & (36)\end{matrix}$

[0193] In equation (36), a control rule is deduced based on theassumptions of the following equations (37), (38). $\begin{matrix}{{\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)} = 0} & (37)\end{matrix}$

[0194] Consequently, a transfer function W(σ) from a target speed ratioG* to the speed ratio G is expressed by the following equation (39).$\begin{matrix}{{W(s)} = \frac{{k_{1} \cdot s} - k_{0}}{s^{3} + {k_{2} \cdot s^{2}} + {k_{1} \cdot s} + k_{0}}} & (39)\end{matrix}$

[0195] where, k₀, k₁, k₂=constants, and s=Laplacian operator.

[0196] The assumptions of the equation (6) and equation (7) are exactlythe same as designing the control system considering that the componentof velocity during a speed change transient state is zero. Thecoefficient f of equation (36) is time-variaint, and it exhibits anonlinear variation with respect to the gyration angle σ. Therefore,when the assumptions specified by the equation (6) and equation (7) donot hold, the response of the speed ratio variation relative to thecontrol output of the controller 80 is not linear.

[0197] For example, referring to FIG. 21, the response of the real speedratio G when the target speed ratio is changed from a speed ratio G₀ forhigh speed to a speed ratio G₁ for low speed in the prior art tends tobe faster in the early stage and tends to be delayed in the latter stageof the speed change, as compared to a linear system W(σ) shown by abroken line in the diagram. The response of the real speed ratio G whenthe target speed ratio is changed from the speed ratio G₁ for low speedto the speed ratio G₀ for high speed tends to be faster in the latterhalf of the speed change.

[0198] Thus, if the trackability of the real speed ratio relative to thevariation of target speed ratio changes, the driver will experience anuncomfortable feeling during a speed change. Such a difference intrackability is based on the assumptions of the equation (6) andequation (7).

[0199] In the first and second embodiments, the coefficient computingunit 101 first computes the time-variant coefficient f The timedifferential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0200] of the partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0201] which was assumed to be zero in the equation (37) according tothe prior art example, is computed by the partial differential computingunit 104 from the coefficient f, the displacement y of the trunnion andthe gyration angle φ. Moreover, the time differential {dot over (f)} ofthe coefficient which was assumed to be zero in the equation (38)according to the prior art example, is computed by the coefficientdifferential computing unit 105 from the displacement y, gyration angleφ and the rotation speed ω_(c0) of the output disks 18B, 20B. Usingthese values, the equivalent input computing unit 106 calculates theequivalent input u_(eq), and the displacement computing unit 111determines the command signal u using the equivalent input u_(eq), sothe response of the real variation amount z relative to the target valuez* always coincides with predetermined characteristics. Therefore, thespeed change response is neither faster nor slower than the targetlinear response as it was in the prior art example.

[0202] The control gain which is corrected by the gain correction unit107, i.e., by the partial differential derivative computing unit 104 andthe coefficient differential computing unit 105, is a feedback gain ofthe offset distance y of the trunnion 23 from the neutral position. Ifthis feedback gain is k_(y), the details of the compensation will varydepending on the nature of the target value z*.

[0203] When the target value z is the speed ratio, the relation betweenthe feedback gain k_(y) and the correction amount is expressed by thefollowing equation (40). $\begin{matrix}{k_{y} = {c \cdot \left\{ {a_{2} - \frac{\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)}{\frac{\partial h}{\partial\varphi} \cdot g} - \frac{f}{f \cdot g}} \right\}}} & (40)\end{matrix}$

[0204] where, a₂=constant determined by the link ratio of the precesscam 52 and the mechanical feedback mechanism,

[0205] g=valve gain, and

[0206] c=constant.

[0207] In this case, the term comprising$\frac{\partial h}{\partial\varphi}$

[0208] and the time differential f of the coefficient f are corrected.

[0209] When the target value is the gyration angle φ of the powerrollers 18C, 18D, 20C, 20D as in a third embodiment described next, therelation between the feedback gain k_(y) and correction amount isexpressed by the following equation (41). $\begin{matrix}{k_{y} = {c \cdot \left( {a_{2} - \frac{\overset{.}{f}}{f \cdot g}} \right)}} & (41)\end{matrix}$

[0210] In this case, the term comprising the time differential {dot over(f)}of the coefficient f is corrected.

[0211] Next, the third embodiment of this invention will be described,referring to FIG. 10, FIGS. 11A and 11B.

[0212] The construction of the hardware in this embodiment is identicalto that of the first embodiment. In this embodiment, the controlvariable z is the gyration angle φ of the power rollers 18C, 18D, 20C,20D.

[0213] In FIG. 10, the dynamic characteristic of the variation of thegyration angle φ of the power rollers 18C, 18D, 20C, 20D relative to thedisplacement u of the step motor is expressed by the equation (1) andequation (2) as in the above-mentioned prior art example.

[0214] A coefficient computing unit 201 and a coefficient differentialcomputing unit 204 shown in FIG. 10 correspond to the coefficientcomputing unit 101 and coefficient differential computing unit 105 ofthe first embodiment.

[0215] A target value generating unit 208 calculates a target gyrationangle φ* from the accelerator pedal depression amount APS and therotation speed ω_(c0) of the output disk.

[0216] A target gyration angle differential computing unit 207 as a partof a command value computing unit 200 calculates a differential {dotover (φ)}* of the target gyration angle φ* by the following process.

[0217] First, the vehicle speed VSP is calculated from the rotationspeed ω_(c0) of the output disk by the equation (17).

[0218] Next, the final input rotation speed tω_(l) is calculated usingthe map having the characteristics shown in FIG. 6 from the acceleratorpedal depression amount APS and vehicle speed VSP. Next, a final speedratio t_(G) is calculated by the following equation 42 which correspondsto the equation (18), from the final input rotation speed tω_(l) androtation speed ω_(c0) of the output disks 18B, 20B. $\begin{matrix}{t_{G} = \frac{t\quad \omega_{i}}{\omega_{co}}} & (42)\end{matrix}$

[0219] The final speed ratio t_(G) is then converted to the finalgyration angle tφ using the equation (3) or the map of FIG. 5. Finally,the differential {dot over (φ)}* of the target gyration angle φ* iscalculated from the final gyration angle tφ, using the followingequation (43):

{dot over (φ)}*=−c _(t) ·φ*+c _(t) ·tφ  (43)

[0220] where, c_(t)=cutoff frequency of lowpass filter.

[0221] A gyration angular velocity computing unit 202 calculates thetime differential {dot over (φ)} of the gyration angle φ, i.e., thegyration angle variation rate, from the offset distance y of thetrunnion 23 from the neutral position and the coefficient f using theequation (1).

[0222] The control error computing unit 203 calculates the control errorσ using the gyration angle φ, the gyration angle variation rate {dotover (φ)} and the target gyration angle φ*.

[0223] This calculation is performed based on the relation of thefollowing equation (44) which is similar to the equation (20) of thefirst embodiment.

σ={dot over (σ)}+c ₀·(φ−φ*)  (44)

[0224] where, c₀=first order delay time constant.

[0225] If the control error σ is assumed to be zero, the relationbetween the gyration angle φ, the gyration angle variation rate {dotover (φ)} and the target gyration angle φ* is expressed by the followingequation (45).

{dot over (φ)}=−c₀·φ+c ₀·φ*  (45)

[0226] Equation (45) shows that the gyration angle φ has a first orderdelay response relative to the target gyration angle φ*, when thecontrol error σ is zero.

[0227] A control error compensation amount computing unit 209 calculatesthe control error compensation amount u_(sw) using the same equation(22) as that of the first embodiment from the control error σ.

[0228] An equivalent input computing unit 205 calculates the equivalentinput u_(eq) corresponding to the command signal to the step motor whenthe control error σ is a fixed value, from the gyration angle φ, offsetdistance y of the trunnion 23 from the neutral position, coefficient fand target gyration angle φ*.

[0229] For this calculation, a second differential of the equation (1)is calculated to obtain the following equation (46).

{umlaut over (φ)}={dot over (f)}·y+f·{dot over (y)}  (46)

[0230] Substituting the equation (2) in the equation (46), the followingequation (47) is obtained.

{umlaut over (φ)}={dot over (f)}·y+f·g·(u−a ₁ ·φ−a ₂ ·y)  (47)

[0231] By calculating a second differential of the equation (44), thefollowing equation (48) is obtained.

{dot over (φ)}={umlaut over (σ)}+c ₀ ·{dot over (φ)}−c ₀·{dot over(φ)}*  (48)

[0232] Here, it is assumed that the control error σ is fixed, so thecontrol error differential {dot over (σ)} is zero. Therefore, thefollowing equation (49) is obtained from the equation (48).

{umlaut over (φ)}=−c ₀ ·{dot over (φ)}+c ₀·{dot over (φ)}*  (49)

[0233] If the equation (47) and equation (49) are solved for the commandsignal u of the step motor, the following equation (50) is obtained.$\begin{matrix}{u = {{\left( {a_{2} - \frac{\overset{.}{f}}{f \cdot g}} \right) \cdot y} - {\frac{c_{0}}{f \cdot g} \cdot \left( {\overset{.}{\varphi} - {\overset{.}{\varphi}}^{*}} \right)} + {a_{1} \cdot \varphi}}} & (50)\end{matrix}$

[0234] The equivalent input computing unit 205 inputs the command valueu of the step motor calculated by the equation (50) as an equivalentinput u_(eq) into a displacement computing unit 210. In the abovementioned prior art example, the differential {dot over (f)} of thecoefficient f was assumed to be zero, but in this embodiment, theequivalent input u_(eq) is calculated using the value {dot over (f)}which the coefficient differential computing unit 204 of the gaincorrection unit 206 calculated, as shown in the equation (50).

[0235] The displacement computing unit 210 outputs the sum of thecontrol error compensation amount u_(sw) which the control errorcompensation amount computing unit 209 calculated, and the equivalentinput u_(eq) which the equivalent input computing unit 106 calculated,as the step motor displacement command value u to the step motor of theTCVT 10.

[0236] Next, the speed ratio control routine which the controller 80performs in order to realize the above control will be describedreferring to FIGS. 11A and 11B. This routine is performed at an intervalof twenty milliseconds.

[0237] In FIGS. 11A and 11B, identical numbers are given to steps whichperform the same processing as FIGS. 7A and 7B of the first embodiment,different step numbers being given only to steps which perform differentprocessing from the routine of FIGS. 7A and 7B.

[0238] Referring to FIG. 1A, the steps S1, S3 are identical to the stepsS1, S3 of the first embodiment.

[0239] In a step S104 which replaces the step S4 of the firstembodiment, the final speed ratio t_(G) is calculated by the equation(42) from the final input rotation speed tω_(l) and the rotation speedω_(c0) of the output disks 18B, 20B. The final speed ratio t_(G) isconverted to the final gyration angle tφ by looking up the map of FIG.5.

[0240] In a step S105 which replaces the step S5 of the firstembodiment, the target gyration angle φ* is calculated from theaccelerator pedal depression amount APS and the rotation speed ω_(c0) ofthe output disks.

[0241] In a step S106 which replaces the step S6 of the firstembodiment, the target gyration angle variation rate {dot over (φ)}* iscalculated. Here, the difference between the immediately preceding valueφ*⁻¹ of the target gyration angle φ* calculated on the immediatelypreceding occasion the routine was performed, and the target gyrationangle φ* calculated on the present occasion, is assumed to be thevariation rate {dot over (φ)}*. The variation rate {dot over (φ)}* maybe obtained by differentiating the target gyration angle φ* using apseudo-differentiator, or by directly calculating the variation rate{dot over (φ)}* using the equation (43).

[0242] In the first embodiment, the control variable z is computed inthe step S7, but in this embodiment, the gyration angle φ correspondingto the control variable z is read in the step S1, so the step S7 isomitted.

[0243] The following step S8 is the same as that of the firstembodiment.

[0244] In the first embodiment, the partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0245] and its time differential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0246] is computed in the step S9, but in this embodiment, these valuesare not used, so the step S9 is omitted.

[0247] In a step S11O which replaces the step S10, the coefficient f andits time differential {dot over (f)} are calculated. The calculationprocess is the same as that of the step S10 of the first embodiment, butin this embodiment, the step S9 is omitted, so in the step S110,$\frac{\partial f}{\partial\varphi}$

[0248] is calculated by the equation (13) and$\frac{\partial f}{\partial\omega_{co}}$

[0249] is calculated by the equation (14), and the calculation of theequation (12) is performed.

[0250] In a step S11 which replaces the step S11, the gyration anglevariation rate {dot over (φ)} is calculated, using the equation (1),from the offset distance y of the trunnion 23 from the neutral positionread in the step S1 and the coefficient f calculated in the step S110.

[0251] Next, referring to FIG. 11B, steps S12-S18 which set the controlerror compensation amount u_(sw) are identical to those of the stepsS12-S18 of the first embodiment.

[0252] In a step S119 which replaces the step S19 of the firstembodiment, the command value u to the step motor is calculated usingthe equation (50), and the equivalent input u_(eq) is set equal to thecommand value u.

[0253] A step S20 is identical to the step S20 of the first embodiment,and the sum of the control error compensation amount u_(sw) andequivalent input u_(eq) is computed as the command value u to the stepmotor. After the processing of the step S20, the controller 80terminates the routine.

[0254] Due to the processing of this control routine, even when thecontrol variable is the gyration angle φ, regarding the variationrelative to the target gyration angle φ* of the gyration angle φ, anessentially fixed response relative to the displacement of the stepmotor is obtained.

[0255] Next, a fourth embodiment of this invention will be describedreferring to FIGS. 12-14.

[0256] The construction of the hardware in this embodiment is identicalto that of the third embodiment, only the details of the processing ofthe controller 80 being different.

[0257] In this embodiment, the speed ratio G of the TCVT 10 is set tothe control variable z.

[0258] The controller 80 is provided with a coefficient computing unit301, a gain correction unit 305 comprising a partial differentialderivative computing unit 302 and a coefficient differential computingunit 303, a command value computing unit 308 comprising a displacementcomputing unit 304 and a control variable second differential targetvalue computing unit 306, and a target value generating unit 307, asshown in FIG. 12.

[0259] Of these, the coefficient computing unit 301, the partialdifferential derivative computing unit 302, the coefficient differentialcomputing unit 303 and the target value generating unit 307 areidentical to the coefficient computing unit 101, partial differentialderivative computing unit 104, coefficient differential computing unit105 and target value generating unit 109 of the first embodiment.

[0260] The displacement computing unit 304 calculates the step motordisplacement command value u from the gyration angle φ of the powerroller, offset distance y of the trunnion 23 from the neutral position,coefficient f calculated by the coefficient computing unit 301, partialdifferential derivative ∂h/∂φ calculated by the partial differentialderivative computing unit 302, coefficient differential {dot over (f)}calculated by the coefficient differential computing unit 303, andcontrol variable second differential target value v calculated by thecontrol variable second differential target value computing unit 306.

[0261] The second differential derivative of the control variable z isidentical to that of the equation (25) of the first embodiment.

[0262] Substituting the equation (2) in the equation (25), the followingequation (51) is obtained. $\begin{matrix}\begin{matrix}{\overset{¨}{z} = \quad {{\frac{}{t}{\left( \frac{\partial h}{\partial\varphi} \right) \cdot f \cdot y}} + {\frac{\partial h}{\partial\varphi} \cdot f \cdot y} + {\frac{\partial h}{\partial\varphi} \cdot f} +}} \\{\quad {g \cdot \left( {u - {a_{1} \cdot \varphi} - {a_{2} \cdot y}} \right)}}\end{matrix} & (51)\end{matrix}$

[0263] In the equation (51), if the control variable second differentialtarget value v is input virtually, the relation of the followingequation (52) will be satisfied.

{umlaut over (z)}=v  (52)

[0264] From the equation (51) and equation (52), the following equation(53) is obtained. $\begin{matrix}\begin{matrix}{v = \quad {{\frac{}{t}{\left( \frac{\partial h}{\partial\varphi} \right) \cdot f \cdot y}} + {\frac{\partial h}{\partial\varphi} \cdot f \cdot y} +}} \\{\quad {{\frac{\partial h}{\partial\varphi} \cdot f} + {g \cdot \left( {u - {a_{1} \cdot \varphi} - {a_{2} \cdot y}} \right)}}}\end{matrix} & (53)\end{matrix}$

[0265] If the equation (53) is solved for the step motor displacementcommand value u, the following equation (54) will be obtained.$\begin{matrix}{u = {\frac{v}{\frac{\partial h}{\partial\varphi} \cdot f \cdot g} + {\left\{ {a_{2} - \frac{\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)}{\frac{\partial h}{\partial\varphi} \cdot g} - \frac{f}{f \cdot g}} \right\} \cdot y} + {a_{1} \cdot \varphi}}} & (54)\end{matrix}$

[0266] The differential value {dot over (f)} of the coefficient f of theequation (54) and the time differential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0267] of the partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0268] is a feedback gain related to the offset distance y of thetrunnion 23 from the neutral position. These values are assumed to bezero in the prior art example, respectively, but in this embodiment, thegain correction unit 305 calculates these feedback gains {dot over (f)}and ${\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)},$

[0269] and the displacement computing unit 304 calculates the step motordisplacement command value u using these values.

[0270] Equation (54) corresponds to the nonlinear function computationshown in FIG. 13A. According to this calculation, the relation betweenthe control variable second differential target value v and controlvariable second differential {umlaut over (z)} is linear, as shown inFIG. 13B.

[0271] Referring again to FIG. 12, the control variable seconddifferential target value computing unit 306 computes the controlvariable second differential target value v from the target controlvariable z* and the control variable z. As mentioned above, the controlvariable second differential target value v and control variable seconddifferential z have the relation expressed by the equation (52) and FIG.13B.

[0272] Therefore, as shown in FIG. 13C, a closed loop system wherein thecontrol variable z has a linear response relative to the target controlvariable z* is designed by applying a linear controller K(s). Aproportional differential controller (PD controller) is used for thecontroller K(s). The processing by the PD controller is expressed by thefollowing equation (55).

v=−k _(D) ·{dot over (z)}−k _(P) ·z+k _(P) ·z*  (55)

[0273] where, k_(P), k_(D) control constants.

[0274] The control variable differential {dot over (z)} is calculated bythe equation (16). The following equation (56) is obtained from theequation (51) and equation (55).

{umlaut over (z)}=−k _(D) ·{dot over (z)}−k _(P) ·z+k _(P) ·z*  (56)

[0275] Thus, the dynamic characteristics of the control variable zrelative to the target control variable z* have linear characteristicsas shown in the equation (56). The control constants k_(P), k_(D) aredesigned so that the equation (56) has stable, desired characteristics.

[0276] Next, the speed ratio control routine performed by the controller80 will be described referring to FIG. 14. This routine is performed atan interval of twenty milliseconds. The control variable z is the speedratio G of the TCVT.

[0277] The steps S1-S5 and steps S7-S11 are identical to the steps S1-S5and steps S7-S11 of the first embodiment. In this embodiment, thedifferential {dot over (z)}* of the target control variable z* is notused, so the step S6 of the first embodiment is omitted.

[0278] In a step S40 following the step S11, a deviation e of the targetcontrol variable z* and control variable z is calculated by thefollowing equation (57).

e=z*−z  (57)

[0279] In a following step S41, the control variable second differentialtarget value v is calculated by the following equation (58). Theequation (58) is an equation deduced from the equation (55) and equation(57).

v=k _(P) ·e−k _(D) ·{dot over (z)}  (58)

[0280] The following step S18 is the same as the step S18 of the firstembodiment.

[0281] In a following step S43, the step motor command value u iscalculated by the equation (54).

[0282] After the processing of the step S43, the controller 80terminates the routine.

[0283] Due to the execution of the above routine, the dynamiccharacteristics of the control variable z relative to the target controlvariable z* are the linear characteristics shown by the equation (55).

[0284] This embodiment can also be applied to the same IVT as in thesecond embodiment.

[0285] In control of the IVT, the calculation of the final controlvariable tz is different in the case where the control variable z is theIVT speed ratio i, and the case where the control variable z is theinverse i_(l) of the IVT speed ratio i.

[0286] The control variable z in the power recirculation mode when thecontrol variable z is the IVT speed ratio i, is expressed by theequation (31). The control variable z in the direct mode is expressed bythe equation (6). The final control variable tz is expressed by theequation (32).

[0287] The control variable z in the power recirculation mode when thecontrol variable z is the inverse i_(l) of the IVT speed ratio i isexpressed by the equation (33). The control variable z is the directmode is expressed by the equation (34). The final control variable tz isexpressed by the equation (35).

[0288] Next, a fifth embodiment of this invention will be describedreferring to FIG. 15.

[0289] This embodiment corresponds to the case where the controlvariable z of the fourth embodiment is the gyration angle φ of the powerroller. Therefore, the construction of the hardware is identical to thatof the fourth embodiment.

[0290] The dynamic characteristics of the gyration angle φ relative tothe step motor displacement u are expressed by the equation (1) andequation (2).

[0291] The controller 80 is provided with a coefficient computing unit401, a gain correction unit 404 comprising a coefficient differentialcomputing unit 402, a command value computing unit 407 comprising adisplacement computing unit 403 and a gyration angle second differentialcomputing unit 405, and a target value generating unit 406.

[0292] Of these, the coefficient computing unit 401, coefficientdifferential computing unit 402 and target value generating unit 406 areidentical to the coefficient computing unit 101, coefficientdifferential computing unit 105 and target value generating unit 109 ofthe first embodiment.

[0293] The gyration angle second differential computing unit 405calculates a gyration angle second differential 0 by the equation (47)of the fourth embodiment. [The relation between the gyration anglesecond differential {umlaut over (φ)} and the control variable seconddifferential target value v, is specified by the following equation(59).

{umlaut over (φ)}=v  (59)

[0294] The displacement computing unit 403 performs the followingcalculation.

[0295] The following equation (60) is obtained from the equation (47)and equation (59).

v={dot over (f)}·y+f·g·(u−a ₁ ·φ−a ₂ ·y)  (60)

[0296] If the equation (60) is solved for the displacement u of the stepmotor, the following equation (61) is obtained. $\begin{matrix}{u = {\frac{v}{f \cdot g} + {\left( {a_{2} - \frac{\overset{.}{f}}{f \cdot g}} \right) \cdot y} + {a_{1} \cdot \varphi}}} & (61)\end{matrix}$

[0297] From equation (61), the displacement computing unit 403calculates the command value u of the step motor.

[0298] Also in the equation (61), the differential value {dot over (f)}of the coefficient f which was considered to be zero in the aforesaidprior art example, is calculated, and the feedback gain of the offsetdistance y of the trunnion 23 from the neutral position is corrected.Therefore, the relation between the control variable second differentialtarget value v and the gyration angle second differential {umlaut over(φ)} is made linear as shown in FIG. 13B also in this embodiment.

[0299] On the other hand, the target gyration angle second stepdifferential target computing unit 405 calculates the seconddifferential v of the target gyration angle from the target gyrationangle φ* and gyration angle φ. The control variable second differentialtarget value v and gyration angle second differential {umlaut over (φ)}are shown by the equation (59) and FIG. 13B, as mentioned above.

[0300] Therefore, also in this embodiment, the linear controller K(s)shown in FIG. 13C is applied as in the fourth embodiment above, and aclosed loop system in which the gyration angle φ has a linear responserelative to the target gyration angle φ* is designed. A proportionaldifferential controller (PD controller) is used for the controller K(s).The processing by the PD controller is expressed by the followingequation (62). The equation (62) corresponds to the situation where z ofthe equation (55) in the fourth embodiment, is replaced by φ.

v=−k _(D) ·{dot over (φ)}−k _(P) ·φ+k _(P)·φ*  (62)

[0301] The gyration angular velocity 0 is calculated by the equation(1). The following equation (63) is obtained from the equation (62) andequation (58). The equation (63) corresponds to an equation wherein z ofthe equation (56) in the fourth embodiment is replaced by φ.

{umlaut over (φ)}=−k _(D) ·{dot over (φ)}−k _(P) φ+k _(P)·φ*  (63)

[0302] Thus, the dynamic characteristics of the control variable φrelative to the target control variable φ* are the linearcharacteristics shown in the equation (56). The control constants k_(P),k_(D) are designed so that the equation (56) has stable, desiredcharacteristics.

[0303] In order to realize the above control, the controller 80 performsa speed ratio control routine similar to the routine of FIG. 14 in thefourth embodiment, wherein the control variables z, {dot over (z)}, z*,tz are respectively substituted by φ, {dot over (φ)}, φ*, tφ.

[0304] Next, a sixth embodiment of this invention will be describedreferring to FIGS. 16, 17, 18A and 18B.

[0305] In this embodiment, the dynamic characteristics of the step motorare used for the speed ratio control of the TCVT 10. Referring to FIG.16, the step motor has a function to integrate a step motor step rateu_(pps) to convert it into a step number u₀, and as a result, a stepmotor displacement u is generated which is proportional to the stepnumber u₀.

[0306] Here, the relation between the step motor step rate u_(pps) andstep motor step number u₀ can be expressed by the following equation(64).

u₀ =u _(pps)  (64)

[0307] The relation between the step motor step number u₀ and step motordisplacement u can be expressed by the following equation (65).

u=b·u ₀  (65)

[0308] where, b=constant depending on and determined by the cam lead ofthe step motor.

[0309] The dynamic characteristics of the variation of the gyrationangle φ of the power roller relative to the displacement u of the stepmotor, are expressed by the equation (1) and equation (2). The dynamiccharacteristics of the TCVT 10 are expressed by the following equations(66)-(68) by a combination of the equations (64), (65), and theequations (1), (2).

{dot over (φ)}=f·y  (66)

{dot over (y)}=g·(b·u ₀ −a ₁ ·φ−a ₂ ·y)  (67)

{dot over (u)} ₀ =u _(pps)  (68)

[0310] As the parameters a₁, a₂, g of the equation (67) vary accordingto the line pressure P1, they are calculated using a map obtainedbeforehand by a system identification test etc., and are stored in thememory of the controller 80 as constants.

[0311] Next, referring to FIG. 17, the controller 80 is provided with acoefficient computing unit 501, a gain correction unit 506, a commandvalue computing unit 510 and a target value generating unit 508. Thegain correction unit 506 comprises a partial differential derivativecomputing unit 503 and a coefficient differential computing unit 504.The command value computing unit 510 comprises a control variabledifferential computing unit 502, a control variable second differentialcomputing unit 505, a control error computing unit 507 and a speedcomputing unit 509.

[0312] Of these, the coefficient computing unit 501, control variabledifferential computing unit 502, partial differential derivativecomputing unit 503, coefficient differential computing unit 504 andtarget value generating unit 508 are respectively identical to thecoefficient computing unit 101, control variable differential computingunit 102, partial differential derivative computing unit 104,coefficient differential computing unit 105 and target value generatingunit 109 of the first embodiment.

[0313] The control variable second differential computing unit 505calculates the control variable second differential {umlaut over (z)} bythe following equation (69), using the gyration angle φ of the powerroller, offset distance y of the trunnion from the neutral position,step motor step number u₀, rotation speed ω_(c0) of the output disks,and the partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0314] and its time differential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0315] calculated by the partial differential derivative computing unit503. The control variable z in this embodiment is the speed ratio G ofthe TCVT. $\begin{matrix}\begin{matrix}{\overset{¨}{z} = \quad {{{{- \frac{\partial h}{\partial\varphi}} \cdot f \cdot g}{\left\{ {a_{2} - \frac{\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)}{\frac{\partial h}{\partial\varphi} \cdot g} - \frac{\overset{.}{f}}{f \cdot g}} \right\} \cdot y}} +}} \\{\quad {\frac{\partial h}{\partial\varphi} \cdot f \cdot g \cdot \left( {{b \cdot u_{0}} - {a_{1} \cdot \varphi}} \right)}}\end{matrix} & (69)\end{matrix}$

[0316] Equation (69) is an equation obtained by substituting theequations (66)-(68) into the equation (25).

[0317] The step motor step number u₀ is estimated by an observer,estimated by integrating the command value of the step motor step rateu_(pps), or detected directly using a sensor.

[0318] The equation (69) calculates the control variable seconddifferential {umlaut over (z)} by first calculating the differential{dot over (f)} of the coefficient f and the time differential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0319] of the partial differential derivative$\frac{\partial h}{\partial\varphi},$

[0320] both of which were assumed to be zero in the prior art example,in the gain correction unit 506.

[0321] The control error computing unit 507 calculates a control error σby the following equation (70), based on the control variable z, controlvariable differential {dot over (z)}, control variable seconddifferential 2 and target control variable z*. The equation (70)represents a second order oscillation system between the target controlvariable z* and the control variable z.

σ={umlaut over (z)}+2·ζ·ω_(n) ·{dot over (z)}+ω _(n) ²·(z−z*)  (70)

[0322] where, ω_(n)=natural frequency, and

[0323] ζ=damping coefficient of the second order oscillation system.

[0324] The control variable z is calculated using the equation (6) fromthe gyration angle φ. The gyration angle φ is measured using thegyration angle sensor 85 of the first embodiment. Alternatively, it isalso possible to compute it directly by the equation (5) from the outputdisk rotation speed ω_(c0) and input disk rotation speed ω_(c1).

[0325] In equation (70), if the control error σ is assumed to be zero,the relation between the control variable z, control variabledifferential {dot over (z)} and target control variable z*, is expressedby the following equation (71).

{umlaut over (z)}=−2·ζ·ω_(n) ·{dot over (z)}−ω _(n) ² ·z+ω _(n) ²·z*  (71)

[0326] As seen from the equation (71), when the control error σ is zero,the control variable z shows a second order delay response depending onthe natural frequency ω_(n) and damping coefficient ζ relative to thetarget control variable z*.

[0327] The speed computing unit 509 calculates the command value u_(pps)from the control error σ by the following equation (72). $\begin{matrix}{u_{pps} = {{- k} \cdot \frac{\sigma}{\sigma }}} & (72)\end{matrix}$

[0328] where, k=switching gain.

[0329] The switching gain k is set equal to a sufficiently large value,e.g., the maximum drive speed of the step motor. Due to this setting,the control error σ converges to zero in a limited time. The controlvariable z when the control error σ is maintained at zero, has thelinear characteristics shown in the equation (71) relative to the targetcontrol variable z*.

[0330] The controller 80 implements the above control by performing thespeed ratio control routine shown in FIGS. 18A to 18B. This routine isperformed at an interval of twenty milliseconds.

[0331] Referring to FIG. 18A, the controller 80, in a step S50, firstreads the gyration angle φ of the power roller, the offset distance y ofthe trunnion from the neutral position, the accelerator pedal depressionamount APS, the output disk rotation speed ω_(c0), input disk rotationspeed ω_(c1) and line pressure P1 from the signal input from eachsensor. The relation between the output disk rotation speed ω_(c0),power roller rotation speed ω_(pr) and input disk rotation speed ω_(c1)is expressed by the equations (27), (28).

[0332] In a following step S51, the controller 80 calculates the vehiclespeed VSP by the equation (17).

[0333] In a following step S52, the final input rotation speed to, isdetermined by looking up the map of FIG. 6 from the accelerator pedaldepression amount APS and vehicle speed VSP.

[0334] In a following step S53, the final control variable tz iscalculated by the equation (18), from the final input rotation speed tω₁and the rotation speed ω_(c0) of the output disks 18B, 20B.

[0335] In a following step S54, the target control variable z* isobtained by processing the final control variable tz by the lowpassfilter of the equation (19).

[0336] In a following step S55, the differential {dot over (z)}* of thetarget control variable z* is calculated by the same process as in thestep S6 of the first embodiment.

[0337] In a following step S56, the control variable z is calculatedfrom the input disk rotation speed ω_(c1) and output disk rotation speedω_(c0). As mentioned above, the control variable z is calculated by theequation (5) from the speed ratio G of the TCVT 10.

[0338] In a following step S57, the output disk rotation acceleration{dot over (ω)}_(c0) is calculated. This calculation is performed by theequation (29) as the difference between the immediately preceding valueω_(c0−1) of the output disk rotation speed ω_(c0) read on theimmediately preceding occasion the routine was performed, and the outputdisk rotation speed ω_(c0) read on the present occasion the routine isperformed. This calculation may be performed using apseudo-differentiator or an observer.

[0339] In a following step S58, the partial differential derivative$\frac{\partial h}{\partial\varphi}$

[0340] is calculated by the equation (7) from the gyration angle φ ofthe power roller. The partial differential derivative$\frac{\partial^{2}h}{\partial\varphi^{2}}$

[0341] is calculated by the equation (10). Also,$\frac{\partial f}{\partial\omega_{co}}$

[0342] is calculated by the equation (14). Also,$\frac{\partial f}{\partial\varphi}$

[0343] is calculated by the equation (13) from the gyration angle φ ofthe power roller, and the output disk rotation speed ω_(c0). Thesecalculations may be performed by referring to maps prestored in thecontroller 80.

[0344] In a following step S59, the coefficient f is calculated by theequation (4) from the output disk rotation speed ω_(c0) and gyrationangle φ of the power roller. The time differential {dot over (f)} of thecoefficient f is calculated by the equation (12) from$\frac{\partial f}{\partial\omega_{co}},\frac{\partial f}{\partial\varphi},$

[0345] the output disk rotation acceleration {dot over (ω)}_(c0), thecoefficient f and the distance y of the trunnion from he neutralposition.

[0346] In a following step S60, the control variable differential {dotover (z)} is calculated using the equation (16) from$\frac{\partial f}{\partial\varphi},$

[0347] the coefficient f and offset distance y of the trunnion.

[0348] Next, referring to FIG. 18B, in a step S61 following the stepS60, the controller 80 calculates the parameters a₁, a₂, g from the linepressure PI by looking up maps shown in FIGS. 8A-8C.

[0349] In the following step S62, using the equation (69), the controlvariable second differential {umlaut over (z)} is calculated from thegyration angle φ of the power roller, offset distance y of the trunnion,step motor step number u₀, output disk rotation speed ω_(c0) and timedifferential$\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)$

[0350] of the partial differential derivative$\frac{\partial h}{\partial\varphi}.$

[0351] In a following step S63, the control error σ is calculated usingthe equation (70) from the control variable second differential {umlautover (z)}, control variable differential {dot over (z)}, controlvariable z and target control variable z*.

[0352] The process from following steps S64 to S68 is related to thecalculation of the command value U_(pps) by the equation (72).

[0353] First, in a step S64, the controller 80 determines whether or notthe control error σ is a negative value. When the control error σ is anegative value, the controller 80 performs the processing of a step S65.When the control error σ is not a negative value, the controller 80determines whether or not the control error σ is a positive value in astep S66. When the control error σ is a positive value, the controller80 performs the processing of a step S67, and when the control error σis not a positive value, i.e., in the case of zero, the processing of astep S68 is performed.

[0354] In the step S65, the step motor speed command value u_(pps) isset equal to a constant k_(s). The constant k_(s) is a valuecorresponding to the maximum displacement of the step motor 52. In thestep S67, the step motor speed command value u_(pps) is set equal to aconstant −k_(s). In the step S68, the step motor speed command valueu_(pps) is set to zero.

[0355] In a final step S69, the controller 80 integrates the step motorspeed command value u_(pps) by the following equation (73) to computethe step motor step number u₀.

u ₀ =u ⁰⁽⁻¹⁾ +T·u _(pps)  (73)

[0356] where, u⁰⁽⁻¹⁾=step motor step number u₀ calculated on theimmediately preceding occasion the routine was executed, and

[0357] T=execution interval of routine=twenty milliseconds.

[0358] Due to the execution of the above control routine, the dynamiccharacteristics of the control variable z relative to the target controlvariable z* are linear. Therefore, regardless of conditions such as thepresent speed ratio or the variation amount between the present speedratio and the target speed ratio, an effectively constant speed changeresponse is obtained regarding the speed ratio variation to any targetspeed ratio.

[0359] This embodiment can also be applied to speed ratio control of theinfinitely variable transmission (IVT) as was described in the secondembodiment.

[0360] In this case, the control variable z can be made the IVT speedratio i, or the inverse i₁ of the IVT speed ratio i. In any case, thetarget value generating unit 508 calculates the target control variablez* from the accelerator pedal depression amount APS detected by theaccelerator pedal depression amount sensor 81, and the IVT output shaftrotation speed ω_(l0).

[0361] The control variable z in the power recirculation mode when thecontrol variable z is the IVT speed ratio i, is expressed by theequation (31) as in the second embodiment.

[0362] The control variable z in the direct mode is expressed by theequation (6) as in the second embodiment.

[0363] The control variable z in the power recirculation mode when thecontrol variable z is the inverse i_(l) of an IVT speed ratio i isexpressed by the equation (33) as in the second embodiment. The controlvariable z in the direct mode is expressed by the equation (34) as inthe second embodiment.

[0364] Next, a seventh embodiment of this invention will be describedreferring to FIG. 19. In this embodiment, the control variable z in thesixth embodiment is set to the gyration angle φ of the power roller asin the third embodiment. The construction of the hardware is identicalto that of the sixth embodiment.

[0365] The dynamic characteristics of the TCVT 10 are expressed by theequations (66)-(68), as in the sixth embodiment above.

[0366] Referring to FIG. 19, the controller 80 comprises a coefficientcomputing unit 601, a gain correction unit 605, a command valuecomputing unit 609 and a target value generating unit 607. The gaincorrection unit 605 comprises a coefficient differential computing unit603.

[0367] The command value computing unit 609 comprises a gyration angularvelocity computing unit 602, a gyration angular acceleration computingunit 604, a control error computing unit 606 and a speed computing unit608.

[0368] The coefficient computing unit 601 and the coefficientdifferential computing unit 603 are identical to the coefficientcomputing unit 101 and coefficient differential computing unit 105 ofthe first embodiment.

[0369] The gyration angular velocity computing unit 602 and the targetvalue generating unit 607 are identical to the target value generatingunit 208 and gyration angular velocity computing unit 202 of the thirdembodiment.

[0370] The gyration angular acceleration computing unit 604 calculatesthe gyration angular acceleration {umlaut over (φ)} from the gyrationangle φ of the power roller, offset distance y of the trunnion, stepmotor step number u₀ and coefficient f. If the equation (67) issubstituted in the equation (46) which represents the gyration angularacceleration {umlaut over (φ)}, the following equation (74) is obtained.$\begin{matrix}{\overset{¨}{\varphi} = {{f \cdot g \cdot \left( {a_{2} + \frac{\overset{.}{f}}{f \cdot g}} \right) \cdot y} + {f \cdot g \cdot \left( {{c \cdot u_{0}} - {a_{1} \cdot \varphi}} \right)}}} & (74)\end{matrix}$

[0371] where, c=constant.

[0372] The step motor step number u₀ in the equation (74) is estimatedby an observer, or is estimated by integrating the step motor step ratecommand value u_(pps). In the equation (74), the coefficient of theoffset distance y of the trunnion is corrected using the differentialvalue {dot over (f)} of the coefficient f, which was assumed to be zeroin the prior art example. This correction is performed by the gaincorrection unit 605.

[0373] The control error computing unit 606 calculates the control errorσ from the gyration angle φ, gyration angular velocity φ, gyrationangular acceleration {umlaut over (φ)} and target gyration angle φ*.

[0374] The relation between the control error σ, gyration angle φ,gyration angular velocity {dot over (φ)}, gyration angular acceleration{umlaut over (φ)} and target gyration angle φ* is specified by thefollowing equation (75), as in the case of equation (70) of the sixthembodiment.

σ={umlaut over (φ)}+2·ζ·ω_(n) ·{dot over (φ)}+ω _(n) ²·(φ−φ*)  (75)

[0375] where, ω_(n)=natural frequency, and

[0376] ζ=damping coefficient.

[0377] The gyration angle φ of the equation (75) is detected by thegyration angle sensor. However, it is also possible to compute the TCVTspeed ratio G by the equation (5) from the output disk rotation speedω_(c0) and input disk rotation speed ω_(c1), and calculate the gyrationangle φ using the map shown in FIG. 5.

[0378] When the control error σ is zero, the relation between thegyration angle φ, gyration angular velocity {dot over (φ)}, gyrationangular acceleration {umlaut over (φ)} and target gyration angle φ* isexpressed by the following equation (76).

{umlaut over (φ)}=−2·ζ·ω_(n)·{dot over (φ)}−ω_(n) ²·φ+ω_(n) ²·φ*  (76)

[0379] As shown in equation (76), when the control error σ is zero, thegyration angle φ shows a second order delay response depending on thenatural frequency ω_(n) and damping coefficient ζ relative to the targetgyration angle φ*.

[0380] The speed computing unit 608 computes the command value u_(pps)from the control error F.

[0381] The relation between the control error C and command valueu_(pps) is specified by the equation (72), which is identical to thesixth embodiment. When the control error σ is zero, the dynamiccharacteristics of the gyration angle φ relative to the target gyrationangle φ* are linear characteristics expressed by the equation (76).

[0382] The controller 80 realizes the above control by performing thespeed ratio control routine shown in FIGS. 20A and 20B. This routine isperformed at an interval of twenty milliseconds.

[0383] Steps S70-S72 are identical to the steps S1-S3 of the thirdembodiment, and steps S73 and S74 are identical to the steps S104 andS105 of the third embodiment.

[0384] In a following step S77, the output disk rotation acceleration{dot over (ω)}_(c0) is calculated by an identical process to the step S8of the first embodiment.

[0385] In a following step S79, the coefficient f and its timedifferential {dot over (f)} are calculated in an identical process tothe step S110 of the third embodiment.

[0386] In a following step S80, the gyration angle variation rate {dotover (φ)} is calculated in an identical process to the step S111 of thethird embodiment.

[0387] In a following step S81, the parameters a₁, a₂, g are calculatedfrom the line pressure P1 by looking up the maps shown in FIGS. 8A-8C asin the step S61 of the sixth embodiment.

[0388] In a following step S82, the gyration angular acceleration{umlaut over (φ)} is calculated by using the equation (74).

[0389] In a following step S83, the control error σ is calculated byusing the equation (75).

[0390] The following steps S84-S89 are identical to those of the stepsS64-S69 of the sixth embodiment.

[0391] Due to the above control procedure, the dynamic characteristicsof the gyration angle φ are made linear relative to the target controlvariable φ*.

[0392] Therefore, regarding the variation of the gyration angle φ to thetarget gyration angle φ*, a substantially constant response is obtainedrelative to the displacement of the step motor.

[0393] The contents of Tokugan 2001-224122, with a filing date of Jul.25, 2001 in Japan, are hereby incorporated by reference.

[0394] Although the invention has been described above by reference tocertain embodiments of the invention, the invention is not limited tothe embodiments described above. Modifications and variations of theembodiments described above will occur to those skilled in the art, inlight of the above teachings.

[0395] The embodiments of this invention in which an exclusive propertyor privilege is claimed are defined as follows:

What is claimed is:
 1. A control device of a toroidal continuouslyvariable transmission for a vehicle, the vehicle comprising anaccelerator pedal, and the toroidal continuously variable transmissioncomprising an input disk, an output disk, a power roller which transmitstorque between the input disk and the output disk, a trunnion whichsupports the power roller free to rotate, the trunnion comprising atrunnion shaft, the power roller varying a gyration angle (0) accordingto a displacement (y) of the trunnion in the direction of the trunnionshaft to vary a speed ratio of the input disk and output disk, and anoil pressure actuator which drives the trunnion in the direction of thetrunnion shaft, the device comprising: a control valve which suppliesoil pressure to the oil pressure actuator; a mechanical feedbackmechanism connecting the trunnion and the control valve to feed back thedisplacement of the trunnion to the control valve; a valve actuatorwhich controls the control valve according to a command value (u); asensor which detects a rotation speed (ω_(c0)) of the output disk; asensor which detects a depression amount (APS) of the accelerator pedal;a sensor which detects the gyration angle (φ) of the power roller; asensor which detects the displacement (y) of the trunnion in thedirection of the trunnion shaft; and a programmable controllerprogrammed to: calculate a target control variable (z*) which is atarget value of a control variable (z) being an object of control, basedon the accelerator pedal depression amount (APS) and the output diskrotation speed (ω_(c0)); calculate a time-variant coefficient (f)representing the relation between the displacement (y) of the trunnionin the direction of the trunnion shaft and a variation rate ({dot over(φ)}) of the gyration angle (φ) of the power roller; calculate a firsttime differential ({dot over (f)}) which is a time differential of thetime-variant coefficient (f); and determine the command value (u) byapplying a control gain based on the first time differential ({dot over(f)}).
 2. The control device as defined in claim 1, wherein thecontroller is further programmed to calculate a first partialdifferential derivative$\left( \frac{\partial h}{\partial\varphi} \right)$

with respect to the gyration angle (φ) of a function h(φ), the functionh(φ) showing the relation between the gyration angle (φ) and the controlvariable (z), and a second time differential$\left( {\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)} \right)$

which is a time differential of the first partial differentialderivative $\left( \frac{\partial h}{\partial\varphi} \right),$

and determine the control gain based on the first time differential (I)and the second time differential$\left( {\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)} \right).$


3. The control device as defined in claim 2, wherein the controller isfurther programmed to calculate a third time differential ({dot over(z)}) which is a time differential of the control variable (z), from thefirst partial differential derivative$\left( \frac{\partial h}{\partial\varphi} \right),$

the coefficient (f) and the displacement (y) of the trunnion in thedirection of the trunnion shaft, calculate a control error (σ) of a realcontrol variable (z) with respect to a predetermined linearcharacteristic of the control variable (z) from the real controlvariable (z), the third time differential ({dot over (z)}) and thetarget control variable (z*), calculate a control error correctionamount (u_(sw)) causing the control error (σ) to decrease, calculate afourth time differential ({dot over (z)}*) which is a time differentialof the target control variable (z*), calculate an equivalent input value(u_(eq)) corresponding to an input value to the valve actuator causingthe control error (σ) to be constant, from the fourth time differential({dot over (z)}*), the third time differential ({dot over (z)}), thedisplacement (y) of the trunnion in the direction of the trunnion shaft,the gyration angle (φ), the coefficient (f), the first time differential{dot over (f)}) and the first partial differential derivative$\left( \frac{\partial h}{\partial\varphi} \right),$

and determine the command value based on the sum of the control errorcorrection amount (u_(sw)) and the equivalent input value (u_(eq)). 4.The control device as defined in claim 1, wherein the control variable(z) is the gyration angle (φ) of the power roller, the target controlvariable (z*) is a target gyration angle (φ) which is a target value ofthe gyration angle (φ), and the controller is further programmed tocalculate a gyration angle variation rate ({dot over (φ)}), being a timedifferential of the gyration angle (φ), from the coefficient (f) and thedisplacement (y) of the trunnion in the direction of the trunnion shaft,calculate a control error (σ) of a real gyration angle (φ) with respectto a predetermined linear characteristic of the gyration angle (φ). fromthe gyration angle (φ), the gyration angle variation rate ({dot over(φ)}) and the target gyration angle (φ*), calculate a control errorcorrection amount (u_(sw)) causing the control error (σ) to decrease,calculate the target gyration angle variation rate (φ*) which is a timedifferential of the target gyration angle (φ*), calculate an equivalentinput value (u_(eq)) which corresponds to the input value to the valveactuator causing the control error (σ) to be constant, from the targetgyration angle variation rate (φ*), the gyration angle variation rate({dot over (φ)}), displacement (y) of the trunnion in the direction ofthe trunnion shaft, the gyration angle (φ) and the coefficient (f), anddetermine the command value (u) based on the sum of the control errorcorrection amount (u_(sw)) and the equivalent input value (u_(eq)). 5.The control device as defined in claim 2, wherein the controller isfurther programmed to calculate a control variable second differentialtarget value (v) when a dynamic characteristic of the variation of thecontrol variable (z) with respect to the target control variable (z*)coincides with a predetermined linear characteristic, from the targetcontrol variable (z*) and the control variable (z), and determine thecommand value (u) causing the dynamic characteristic of the variation ofthe control variable (z) with respect to the target control variable(z*) to coincide with the predetermined linear characteristic, from thecontrol variable second differential (v), the first partial differentialderivative $\left( \frac{\partial h}{\partial\varphi} \right),$

the second time differential$\left( {\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)} \right),$

do the coefficient (f) the displacement (y) of the trunnion in thedirection of the trunnion shaft, and the gyration angle (φ).
 6. Thecontrol device as defined in claim 1, wherein the control variable (z)is the gyration angle (φ) of the power roller, the target controlvariable (z*) is a target gyration angle (φ) which is a target value ofthe gyration angle (φ), and the controller is further programmed tocalculate a control variable second differential target value (v) when adynamic characteristic of the variation of the control variable (z) withrespect to the target control variable (z*) coincides with apredetermined linear characteristic, from the target gyration angle (φ*)and the gyration angle (φ), and determine the command value (u) causingthe dynamic characteristic of the variation of the gyration angle (φ)with respect to the target gyration angle (φ*) to coincide with thepredetermined linear characteristic, from the control variable seconddifferential (v), the coefficient (f), the first time differential ({dotover (f)}), the displacement (y) of the trunnion in the direction of thetrunnion shaft, and the gyration angle (φ).
 7. The control device asdefined in claim 2, wherein the controller is further programmed tocalculate a control variable time differential ({dot over (z)}) which isa time differential of the control variable (z), from the coefficient(f), the displacement (y) of the trunnion in the direction of thetrunnion shaft, and the first partial differential derivative$\left( \frac{\partial h}{\partial\varphi} \right),$

calculate a control variable second differential ({umlaut over (z)})from the coefficient (f), the first time differential (f), the gyrationangle (φ), the displacement (y) of the trunnion in the direction of thetrunnion shaft, the command value (u), the first partial differentialderivative $\left( \frac{\partial h}{\partial\varphi} \right)$

and the second time differential$\left( {\frac{}{t}\left( \frac{\partial h}{\partial\varphi} \right)} \right),$

calculate a control error (I corresponding to a deviation of a dynamiccharacteristic of the variation of the control variable (z) with respectto the target control variable (z*) from a predetermined linearcharacteristic, based on the target control variable (z*), the controlvariable (z), the control variable time differential ({dot over (z)})and the control variable second time differential ({umlaut over (z)}),and determine the command value (u) to cause the control error (σ) todecrease.
 8. The control device as defined in claim 1, wherein thecontrol variable (z) is the gyration angle (φ), the target controlvariable (z*) is a target gyration angle (φ*) which is a target value ofthe gyration angle (φ), and the controller is further programmed tocalculate a gyration angular velocity ({dot over (φ)}) from thecoefficient (I and the displacement (y) of the trunnion in the directionof the trunnion shaft, calculate a gyration angular acceleration({umlaut over (φ)}) from the coefficient (f) the displacement (y) of thetrunnion in the direction of the trunnion shaft, the gyration angularvelocity ({dot over (φ)}), the command value (u) and the first timedifferential ({dot over (f)}), calculate a control error (σ)corresponding to a deviation of a dynamic characteristic of thevariation of the gyration angle (φ) with respect to the target gyrationangle (φ*) from a predetermined linear characteristic, based on thetarget gyration angle (φ*), the gyration angle (φ), the gyration angularvelocity ({dot over (φ)}) and the gyration angular acceleration ({umlautover (φ)}), and determine the command value (u) to cause the controlerror (σ) to decrease.
 9. A control device of a toroidal continuouslyvariable transmission for a vehicle, the vehicle comprising anaccelerator pedal, and the toroidal continuously variable transmissioncomprising an input disk, an output disk, a power roller which transmitstorque between the input disk and the output disk, a trunnion whichsupports the power roller free to rotate, the trunnion comprising atrunnion shaft, the power roller varying a gyration angle (φ) accordingto a displacement (y) of the trunnion in the direction of the trunnionshaft to vary a speed ratio of the input disk and output disk, and anoil pressure actuator which drives the trunnion in the direction of thetrunnion shaft, the device comprising: means for supplying oil pressureto the oil pressure actuator; means for connecting the trunnion and thecontrol valve to feed back the displacement of the trunnion to thecontrol valve; means for controlling the supplying means according to acommand value (u); means for detecting a rotation speed (ω_(c0)) of theoutput disk; means for detecting a depression amount (APS) of theaccelerator pedal; means for detecting the gyration angle (φ) of thepower roller; means for detecting the displacement (y) of the trunnionin the direction of the trunnion shaft; means for calculating a targetcontrol variable (z*) which is a target value of a control variable (z)being an object of control, based on the accelerator pedal depressionamount (APS) and the output disk rotation speed (ω_(c0)); means forcalculating a time-variant coefficient (f) representing the relationbetween the displacement (y) of the trunnion in the direction of thetrunnion shaft and a variation rate ({dot over (φ)}) of the gyrationangle (φ) of the power roller; means for calculating a first timedifferential ({dot over (f)}) which is a time differential of thetime-variant coefficient (f); and means for determining the commandvalue (u) by applying a control gain based on the first timedifferential ({dot over (f)}).
 10. A control method of a toroidalcontinuously variable transmission for a vehicle, the vehicle comprisingan accelerator pedal, and the toroidal continuously variabletransmission comprising an input disk, an output disk, a power rollerwhich transmits torque between the input disk and the output disk, atrunnion which supports the power roller free to rotate, the trunnioncomprising a trunnion shaft, the power roller varying a gyration angle(φ) according to a displacement (y) of the trunnion in the direction ofthe trunnion shaft to vary a speed ratio of the input disk and outputdisk, an oil pressure actuator which drives the trunnion in thedirection of the trunnion shaft, a control valve which supplies oilpressure to the oil pressure actuator, a mechanical feedback mechanismconnecting the trunnion and the control valve to feed back thedisplacement of the trunnion to the control valve, and a valve actuatorwhich controls the control valve according to a command value (u), themethod comprising: detecting a rotation speed (ω_(c0)) of the outputdisk; detecting a depression amount (APS) of the accelerator pedal;detecting the gyration angle (φ) of the power roller; detecting thedisplacement (y) of the trunnion in the direction of the trunnion shaft;calculating a target control variable (z*) which is a target value of acontrol variable (z) being an object of control, based on theaccelerator pedal depression amount (APS) and the output disk rotationspeed (ω_(c0)); calculating a time-variant coefficient (f) representingthe relation between the displacement (y) of the trunnion in thedirection of the trunnion shaft and a variation rate ({dot over (φ)}) ofthe gyration angle (φ) of the power roller; calculating a first timedifferential ({dot over (f)}) which is a time differential of thetime-variant coefficient (f); and determining the command value (u) byapplying a control gain based on the first time differential ({dot over(f)}).